CONTEMPORARYMATHEMATICS

American Mathematical Society

538

Topology of Algebraic Varieties and Singularities

Conference in Honor of Anatoly Libgober's 60th BirthdayJune 22–26, 2009

Jaca, Huesca, Spain

José Ignacio Cogolludo-AgustínEriko Hironaka

Editors

American Mathematical SocietyReal Sociedad Matemática Española

Topology of Algebraic Varieties and Singularities

http://dx.doi.org/10.1090/conm/538

American Mathematical SocietyProvidence, Rhode Island

CONTEMPORARYMATHEMATICS

538

Topology of Algebraic Varieties and Singularities

Conference in Honor of Anatoly Libgober's 60th Birthday June 22–26, 2009

Jaca, Huesca, Spain

José Ignacio Cogolludo-Agustín Eriko Hironaka

Editors

American Mathematical Society Real Sociedad Matemática Española

Editorial Board of Contemporary Mathematics

Dennis DeTurck, managing editor

George Andrews Abel Klein Martin J. Strauss

Editorial Committee of the Real Sociedad Matematica Espanola

Pedro Jose Paul Escolano, Director

Luis Alıas Linares Alberto Elduque PalomoEmilio Carrizosa Priego Rosa Marıa Miro-RoigBernardo Cascales Salinas Pablo Pedregal TerceroJavier Duoandikoetxea Zuazo Juan Soler Vizcaıno

2000 Mathematics Subject Classification. Primary 00B99, 14B05, 32S99, 57M99, 14–02,32–02, 51–02, 53–02, 55–02, 57–02.

Library of Congress Cataloging-in-Publication Data

Topology of algebraic varieties and singularities : conference in honor of Anatoly Libgober’s60th birthday, June 22–26, 2009, Jaca, Huesca, Spain / Jose Ignacio Cogolludo-Agustın, ErikoHironaka, editors.

p. cm. — (Contemporary mathematics ; v. 538)Includes bibliographical references.ISBN 978-0-8218-4890-6 (alk. paper)1. Algebraic varieties—Congresses. 2. Algebraic topology—Congresses. 3. Singularities

(Mathematics)—Congresses. I. Libgober, A. (Anatoly), 1949– II. Cogolludo-Agustın, JoseIgnacio. III. Hironaka, Eriko, 1962–

QA612.T66 2011516.3′53—dc22

2010047841

Copying and reprinting. Material in this book may be reproduced by any means for edu-cational and scientific purposes without fee or permission with the exception of reproduction byservices that collect fees for delivery of documents and provided that the customary acknowledg-ment of the source is given. This consent does not extend to other kinds of copying for generaldistribution, for advertising or promotional purposes, or for resale. Requests for permission forcommercial use of material should be addressed to the Acquisitions Department, American Math-ematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests canalso be made by e-mail to reprint-permission@ams.org.

Excluded from these provisions is material in articles for which the author holds copyright. Insuch cases, requests for permission to use or reprint should be addressed directly to the author(s).(Copyright ownership is indicated in the notice in the lower right-hand corner of the first page ofeach article.)

c© 2011 by the American Mathematical Society. All rights reserved.The American Mathematical Society retains all rightsexcept those granted to the United States Government.

Copyright of individual articles may revert to the public domain 28 yearsafter publication. Contact the AMS for copyright status of individual articles.

Printed in the United States of America.

©∞ The paper used in this book is acid-free and falls within the guidelinesestablished to ensure permanence and durability.

Visit the AMS home page at http://www.ams.org/

10 9 8 7 6 5 4 3 2 1 16 15 14 13 12 11

This volume is a small tribute to Anatoly Libgober’s inspiring life-long personal andprofessional contributions to Mathematics, on the occasion of his sixtieth birthday.

Anatoly Libgober(photograph courtesy of Brian Libgober)

Contents

Preface ix

List of Participants xiii

Part I: A Historical Note 1

Development of the Theory of Alexander Invariants in Algebraic Geometryby Anatoly Libgober 3

Part II: Algebraic Geometry and Fundamental Groups 19

Feynman Motives and Deletion-Contraction Relationsby Paolo Aluffi and Matilde Marcolli 21

Classification of Fundamental Groups of Galois Covers of Surfaces of SmallDegree Degenerating to Nice Plane Arrangements

by Meirav Amram, Rebecca Lehman, Robert Shwartz, and Mina

Teicher 65

Homomorphisms between Kahler groupsby Donu Arapura 95

Quasi-Projectivity, Artin-Tits Groups, and Pencil Mapsby Enrique Artal-Bartolo, Jose I. Cogolludo-Agustın, and Daniel

Matei 113

Topology of Plane Algebraic Curves: The Algebraic Approachby Alex Degtyarev 137

Hirzebruch Invariants of Symmetric Productsby Laurentiu Maxim and Jorg Schurmann 163

Fundamental Groups, Alexander Invariants, and Cohomology Jumping Lociby Alexander I. Suciu 179

Part III: Braids and Knots 225

On Reduction Curves and Garside Properties of Braidsby Juan Gonzalez-Meneses 227

Topological Quantum Information, Khovanov Homology and the JonesPolynomial

by Louis H. Kauffman 245

HOMFLYPT Skein Module of Singular Linksby Luis Paris 265

vii

viii CONTENTS

Part IV: Hyperplane Arrangements 277

First Milnor Cohomology of Hyperplane Arrangementsby Nero Budur, Alexandru Dimca, and Morihiko Saito 279

Minimal CW-complexes for Complements to Line Arrangements via DiscreteMorse Theory

by Giovanni Gaiffi, F. Mori, and M. Salvetti 293

The Topology of Hyperplane Arrangementsby Richard Randell 309

Part V: Singularities 319

On ν-Quasi-Ordinary Power Series: Factorization, Newton Trees and Resultantsby E. Artal-Bartolo, Pi. Cassou-Nogues, I. Luengo, and A.

Melle-Hernandez 321

Milnor Fibrations for Real and Complex Singularitiesby Jose Luis. Cisneros-Molina, Jose Seade, and Jawad Snoussi

345

On Homotopy Types of Complements of Analytic Sets and Milnor Fibresby Javier Fernandez de Bobadilla 363

The Milnor Fiber Signature is not Semicontinuousby Dmitry Kerner and Andras Nemethi 369

Principal Analytic Link Theory in Homology Sphere Linksby A. Nemethi, Walter D. Neumann, and A. Pichon 377

On Mixed Brieskorn Varietyby Mutsuo Oka 389

Introduction to Jung’s Method of Resolution of Singularitiesby Patrick Popescu-Pampu 401

Biggest Sharp Polynomial Estimate of Integral Points in Right-Angled Simplicesby Stephen S.-T. Yau, Linda Zhao, and Huaiqing Zuo 433

Preface

The present volume is a collection of surveys and research papers written byinvitation or based on plenary talks given at the conference on “Topology of Alge-braic Varieties”, held in Jaca, Spain from the 22nd to the 26th of June, 2009. Itpresents the contemporary status of a variety of topological problems in algebraicgeometry on the borderline between the singularity theory, knot theory and combi-natorics. The Jaca’s meeting took place on the occasion of Anatoly Libgober 60thbirthday.

In addition to the plenary talks, the conference also had short communicationsand poster sessions, which are not included here, but which contributed significantlyto the wide range of topics covered during the intense week-long meeting.

This volume consists of four parts corresponding to the specific aspects onwhich the conference was focused: Algebraic Geometry and Fundamental Groups,Braids and Knots, Arrangements and Singularities.

There were more than 150 participants at this meeting and the list of invitedparticipants included major contributors in Algebraic Geometry and Singularitytheory and past collaborators of Anatoly’s such as Heisuke Hironaka, Le DungTrang, Donu Arapura, Tatyana Bandman, Denis Cheniot, Alexandru Dimca, StevenSperber, John Wood, Stephen S.-T Yau, and Sergey Yuzvinsky.

The unifying themes of A. Libgober work are the Topology of Algebraic Vari-eties and Singularity theory.

A. Libgober was born in Moscow in the former Soviet Union on March 24, 1949.He attended Moscow University from 1964 until 1970. He studied algebraic geom-etry with Yu. I Manin and I.I. Piatetski-Shapiro. A. Libgober applied to emigrateto Israel in 1971, was denied permission but after active protests was allowed toleave in June 1973. He wrote his Ph.D. dissertation at Tel-Aviv University under B.Moishezon in 1977. After spending one year at the Institute for Advanced Studiesat Princeton he became Assistant Professor at the University of Illinois at ChicagoCircle (later renamed to University of Illinois at Chicago). He was named Professorin 1988. During his tenure he returned several times to the Institute for AdvancedStudy, the Institute des Hautes Etudes Scientifiques (Bures sur Yvette), the MaxPlanck Institute (Bonn, Germany), and the MSRI (Berkeley). He visited HarvardUniversity (1982) and Columbia University (1987-88). He lectured extensively inUSA, Israel, Germany, France, Spain, and Japan. His Ph.D. students thus far areS. Giallamas (1986), J.I. Cogolludo (1999), N. Krylov (2002), and V. Egorin (2004).He also informally advised E. Hironaka during her work on Ph.D. dissertation andwas PostDoc mentor for L. Maxim and R. Waelder.

A. Libgober’s thesis “Topology of algebraic hypersurfaces” studied the prob-lem of identifying the type of smooth algebraic hypersurfaces in projective space

ix

x PREFACE

as differentiable or topological manifolds. This problem attracted much attentionin the case of complex surfaces. However, the higher-dimensional case requirescompletely different approaches. His calculation of the Kervaire invariant of hyper-surfaces provided a link between topology and singularity theory. Later, continuinghis work jointly with J. Wood, he showed the existence of diffeomeorphic completeintersections of different multi-degrees in dimension greater than two. A few yearslater A. Libgober started the study of Alexander invariants of the complementto plane algebraic curves and used methods of knot theory and low-dimensionaltopology for the study of these complements. He proved his divisibility theoremrelating the fundamental group of the complements to the type of singularities ofthe curve. He also found a description of the homotopy type of the complements toplane affine singular curves, gave restrictions on the groups which can appear as thefundamental groups of the complements to plane algebraic curves, developed themultivariable version of Alexander invariants, and developed the use of the Hodgetheoretical methods for these problems. This paved the way to the revival of thisarea of algebraic geometry in the last twenty years. Since then the theory developedin a vast subject of Alexander invariants of quasi-projective varieties and found itsapplications in the theory of arrangements, topology of plane singular curves, studyof Kahler groups, etc. In the early 90’s his joint work with J. Teitelbaum expandedthe scope of the spectacular description by physicists such as P. Candelas, X. de laOssa, P. Font, or L. Parkes on mirror symmetry of quintic hypersurfaces giving theorbifold construction of these mirror partners of Calabi-Yau complete intersections(about the same time L. Borisov-V. Batyrev developed the theory of mirror dualityfor complete intersection, extending V. Batyrev’s mirror duality). A. Libgober con-tinued his work on mathematical foundations of new at the time ideas from physicsin series of joint works with Lev Borisov introducing notion of of elliptic genusfor singular algebraic varieties. This theory of the elliptic genus of varieties Q-Gorenstein singularities, orbifolds, real algebraic varieties and in particular McKaycorrespondence for elliptic genus, found connections with homotopy theory, vertexoperator algebras, modular forms and the moonshine.

Sponsors of Jaca’s conference include the National Science Foundation (NSF),the Spanish Ministerio de Ciencia e Innovacion, the Clay Mathematics Institute,the local Government of Aragon (DGA), the Program Ingenio Mathematica by theSpanish Mathematics Institute, the Red Espanola de Topologıa (RET), the Uni-versities of Illinois (UIC) and Zaragoza (UZ), and the American (AMS), European(EMS), and Spanish (RSME) Mathematical Societies have turned this event into amilestone for this area of mathematics.

This meeting would have not been possible without the dedication shown by theOrganizing Committee: Jose Ignacio Cogolludo, Vladimir Egorin, Eriko Hironaka,Alejandro Melle, Mina Teicher, and Domingo Toledo. The Scientific Committee,formed by Ignacio Luengo, Norbert A’Campo, Victor Batyrev, Joan Birman, Lau-rence Ein, and Jose Marıa Montesinos, made a special effort to find a representativelist of speakers that could attempt to cover the many subjects Anatoly Libgober has

PREFACE xi

contributed to, and that share an interest in Singularity Theory and the Topologyof Algebraic Varieties.

Jose Ignacio Cogolludo-AgustınEriko Hironaka

List of Participants

Norbert A’CampoMathematikUniversitaet BaselRheinsprung 21Basel, CH-4051, Switserlandemail: norbert.acampo@unibas.ch

Haydee Aguilar CabreraInstitut De Mathematiques De LuminyUniversite Aix Marseille IICase 907, 163 Avenue De Luminy,Cedex 9Marseille, 13288, Franceemail: langeh@gmail.com

Paolo AluffiMathematicsFlorida State UniversityTallahassee, FL 32306, USAemail: aluffi@math.fsu.edu

Jaume AmorosMatematica Apl. IUPCETSEIB, Diagonal 64Barcelona, E-08028, Spainemail: jaume.amoros@upc.edu

Donu ArapuraMathematicsPurdue University150 N. University St.W. Lafayette, IN 47907, USAemail: dvb@math.purdue.edu

Fuensanta ArocaInstituto de MatematicasUniversidad Nacional Autonoma deMexicoApartado Postal 273. Admon. decorreos #3Av. Universidad s/n, Lomas deChamilpaCuernavaca, Morelos 62251, Mexicoemail: fuen@matcuer.unam.mx

Enrique Artal BartoloMatematicasUniversidad de ZaragozaC/Pedro Cerbuna 12Zaragoza, 50009, Spainemail: artal@unizar.es

Tatiana BandmanMathematicsBar-Ilan UniversityRamat Gan, 52900, Israelemail: bandman@macs.biu.ac.il

Grazielle Feliciani BarbosaMathematicsICMC - USPRua Carlos del Nero 161Sao Carlos - SP, 13564-420, Brazilemail: gbarbosa@icmc.usp.br

Victor BatyrevMathematical InstituteUniversity of TubingenAuf der Morgenstelle 10Tubingen, D-72076, Germanyemail: victor.batyrev@uni-tuebingen.de

xiii

xiv PARTICIPANTS

Nasreddine BenkafadarMathematicsUniversity of ConstantineBP B5 PTT Djeffal 25100, KhrouConstantine, 25100, Algeriaemail: kafadar@gmx.com

Lev BirbrairMathematicsUniv. Fed. CearaAv. da Universidade, 2853 - BenficaFortaleza, CEP 60020-181, Brazilemail: birb@ufc.br

Maciej Edward BorodzikUniversity of WarsawInstitute of MathematicsBanacha 2Warsaw, 02-097, Polandemail: mcboro@mimuw.edu.pl

Jean-Paul BrasseletIML, CNRSCase 907 LuminyMarseille cedex 9, 13288, Franceemail: jpb@iml.univ-mrs.fr

Mirel Constantin CaibarMathematicsOhio State University231 W 18th AvenueColumbus, OH 43210, USAemail: caibar@math.ohio-state.edu

Antonio CampilloAlgebra, Geometrıa y TopologıaValladolid UniversityFacultad de Ciencias, Prado de laMagdalena s/nValladolid, 47005, Spainemail: campillo@agt.uva.es

Jorge CasanovaCultural CommitteeZaragoza, Spainemail: jorgecasanova@arrakis.es

Catiana CasonattoMathematicsICMC - USPMora de Rubielos, n. 14 Piso: 2, 9Valencia, Valencia 46007, Espanaemail: catianac@icmc.usp.br

Pierrette Cassou-NoguesInstitut de mathematiques de BordeauxUniversite Bordeaux 1351, Cours de la LiberationTalence, 33405, Franceemail: cassou@math.u-bordeaux1.fr

Julio CastellanosAlgebraUCMPlaza de las Ciencias 3Madrid, 28003, Espanaemail: jcaste@mat.ucm.es

Francisco-Jesus Castro-JimenezMatematicas – AlgebraUniversidad de SevillaCampus de Reina MercedesSevilla, 41012, Spainemail: castro@us.es

Clement CaubelEquipe Geometrie et dynamiqueInstitut de Mathematiques de JussieuSite Chevaleret, Case 701PARIS CEDEX 13, 75205, Franceemail: caubel@math.jussieu.fr

Lizandro Sanchez ChallapaMathematicsInstituto de Ciencias Matematicas e deComputacao (ICMC-USP)Rua Cezar Ricome, 33Sao Carlos, Sao Paulo 13560-510, Brazilemail: challapa1874@gmail.com

PARTICIPANTS xv

Qingtao ChenMathematicsUC-Berkeley2299 Piedmont AveBerkeley, CA 94720, USAemail: chenqtao@math.berkeley.edu

Denis CheniotLaboratoire d’Analyse, Topologie etProbabilitesretired from Universite de Provencerue du Canal, Le CasseLe Monetier-les-Bains, 05220, Franceemail: cheniot@cmi.univ-mrs.fr

Hichem ChtiouiMathematiqueFaculte des Sciences de Sfax TunisiaRte Soukra Km 4 Sfax TunisiaSfax, 3018, Tunisiaemail: Hichem.Chtioui@fss.rnu.tn

Jose Luis Cisneros-MolinaInstituto de MatematicasUNAMAv. Universidad S/N, Lomas DeChamilpaCuernavaca, Morelos, 62210, Mexicoemail: jlcisneros@gmail.com

Esther Sanabria CodesalMatematica AplicadaUniversidad Politecnica de ValenciaCamino de Vera s/nValencia, 46025, Spainemail: esanabri@mat.upv.es

Jose Ignacio Cogolludo AgustınMatematicasUniversidad de ZaragozaC/ Pedro Cerbuna, 12Zaragoza, 50009, Spainemail: jicogo@unizar.es

Maria Angelica CuetoMathematicsUC Berkeley970 Evans Hall #3840Berkeley, CA 94720, United Statesemail: macueto@math.berkeley.edu

Miriam Da Silva PereiraMathematicsUniversidade de Sao Paulo- ICMC- SaoCarlosRua Jacinto Favoretto, 822- Apto 23Sao Carlos, 13560-500, Brasilemail: miriamsp@icmc.usp.br

Thais Maria DalbeloMatematicaICMC/USPAv. Trabalhador Sao-carlense, 400Jesuıno de Arruda, 1365 - Ap. 10Sao Carlos, 13560-970, Brazilemail: tdalbelo@icmc.usp.br

Alex DegtyarevMathematicsBilkent UniversityAnkara, 06800, Turkeyemail: degt@fen.bilkent.edu.tr

Alexandru DimcaLaboratoire J.-A. DieudonneUniversity of NiceParc ValroseNice, 06108, Franceemail: dimca@unice.fr

Roi Docampo AlvarezMathematicsUniversity of Illinois at Chicago3425 W Drummond PlChicago, Illinois 60647, USAemail: docampo@math.uic.edu

xvi PARTICIPANTS

Alan DurfeeMathematics and StatisticsMount Holyoke College50 College StreetSouth Hadley, MA 01075, USAemail: adurfee@mtholyoke.edu

Vladimir EgorinMathematicsUniversity of Illinois at Chicago851 S. Morgan StreetChicago, IL 60610, USAemail: vladimir@math.uic.edu

Lawrence EinDepartment of mathematicsUniversity of Illinois at Chicago851 S. Morgan StreetChicago, Illinois 60607, USAemail: ein@uic.edu

Eka ElerdashviliMathematicsGergian Technical UniversityM.KostavaTbilisi, 0128, Georgiaemail: eka.elerdashvili@yahoo.com

Meital EliyahuMath DepartmentBar Ilan UniversityBar Ilan UniversityRamat Gan, 52900, Israelemail: eliyahm@math.biu.ac.il

Daniele FaenziLaboratoire de Mathematiques etApplicationsUniversite de PauAvenue de l’Universite - BP 1155Pau, 64013, Franceemail: daniele.faenzi@univ-pau.fr

Michael FalkDept. of Mathematics and StatisticsNorthern Arizona UniversityBox 5717Flagstaff, AZ 86011-5717, USAemail: michael.falk@nau.edu

Kwai-Man FanMathematicsChung Cheng University168 University RoadMinghsiung, Chiayi 621, Taiwanemail: kmfan@math.ccu.edu.tw

Marıa Cruz Fernandez FernandezAlgebraUniversidad de SevillaC/Teodosio 25Santiponce (Sevilla), 41970, Espanaemail: mcferfer@us.es

Michael FriedmanMathematicsBar-Ilan UniversityHaAlia HashniaRamat Gan, 52253, Israelemail: fridmam@macs.biu.ac.il

James Albert FullwoodMathematicsFlorida State University2006 Sheridan Rd.Tallahassee, FL 32303, United Statesemail: antna@hotmail.com

David GarberDepartment of Applied MathematicsHolon Institute of TechnologyGolomb 52, PO Box 30Holon, 58102, Israelemail: garber@hit.ac.il

PARTICIPANTS xvii

Luis GiraldoGeometrıa y TopologıaUniversidad Complutense de MadridPlaza de las Ciencias 3Madrid, 28040, Spainemail: luis.giraldo@mat.ucm.es

Xavier Gomez-MontMathematicsCIMATXalisco s/n, AP 40Guanajuato, 36240, Mexicoemail: gmont@cimat.mx

Pedro D. Gonzalez PerezAlgebraUniversidad Complutense de MadridPlaza de las Ciencias 3Madrid, 28040, Spainemail: pgonzalez@mat.ucm.es

Manuel Gonzalez VillaAlgebraUCMAlmansa 98, 3 CMadrid, 28040, Spainemail: mgv@mat.ucm.es

Marıa del Rosario Gonzalez-DorregoMathematicsUniversidad Autonoma de MadridFacultad de CienciasCantoblanco-Madrid, 28049, Spainemail: mrosario.gonzalez@uam.es

Juan Gonzalez-MenesesAlgebraUniversidad de SevillaApdo. 1160. 41080-Sevilla.Sevilla, 41002, Spainemail: meneses@us.es

Victor Goryunovof Mathematical SciencesUniversity of LiverpoolPeach streetLiverpool, L69 3BX, UKemail: goryunov@liv.ac.uk

Nivaldo de Goes Grulha Jr.MatematicaUniversidade de Sao Paulo-ICMC-SaoCarlosAv. Trabalhador Sao-carlense, 400CENTRO, Caixa Postal: 66Sao Carlos - SP, 13560-970, Brasilemail: njunior@icmc.usp.br

Amanda C HagerMathematicsUniversity of Iowa14 MacLean HallIowa City, IA 52242, USemail: amanda-hager@uiowa.edu

Helmut Arend HammMath. InstitutWWU MuensterEinsteinstr. 62Muenster, 48149, Germanyemail: hamm@math.uni-muenster.de

Iulia Elena HiricaFaculty of Mathematics andInformaticsUniversity of Bucharest14 Academiei Str.,Bucharest, RO-010014, Romaniaemail: ihirica@fmi.unibuc.ro

Eriko HironakaMathematicsFlorida State UniversityTallahassee, FL 32306-4510, U.S.A.email: hironaka@math.fsu.edu

xviii PARTICIPANTS

Heisuke HironakaMathematicsJAMSCoop Olympia 506, Jingumae 6-35-3,ShibuyakuTokyo, 150-0001, Japanemail: heihiron@gmail.com

Denis IbadulaMathematicsOvidius University, Constanta,RomaniaStr. Fagetului Nr.136, Bl.ST3, Sc.B,ap.17Constanta, 900654, Romaniaemail: denis@univ-ovidius.ro

Ilia ItenbergIRMAUniversite de Strasbourg7 rue Rene DescartesStrasbourg, 67084, Franceemail: itenberg@math.u-strasbg.fr

Milagros IzquierdoMatematiska institutionenLinkoping universitetLinkopings universitetLinkoping, 581 83, Swedenemail: miizq@mai.liu.se

Masaki KasedouDepartment of MathematicsHokkaido UniversityKita 10, Nishi 8, Kita-KuSapporo, 060-0810, Japanemail: kasedou@math.sci.hokudai.ac.jp

Louis Hirsch KauffmanMathematicsUniversity of Illinois at Chicago851 South Morgan StreetChicago, Illinois 60607-7045, USAemail: kauffman@uic.edu

Gary P. KennedyMathematicsOhio State University1760 University DriveMansfield, OH 44906, USAemail: kennedy@math.ohio-state.edu

Dmitry KernerMathematicsBen Gurion University, IsraelShkolnik str.6/28Rehovoth, 76209, Israelemail: kernerdm@math.bgu.ac.il

Cong Trinh LeMathematicsTU KaiserslauternTrippstadter Str. 46Kaiserslautern, 67663, Germanyemail: cle@mathematik.uni-kl.de

Dung Trang LeMathematicsICTPStrada Costiera 11Trieste, 34151, Italyemail: ledt@ictp.it

Rebecca C LehmanMathematicsBar Ilan UniversityDepartment of MathematicsRamat Gan, 52900, Israelemail: rebecca.lehman@gmail.com

Maxim LeyensonMathematicsBar Ilan UniversityBen Gamla. 18Jerusalem, Moshava Yevanit, Israelemail: leyenson@gmail.com

PARTICIPANTS xix

Haijian Kevin LinMathematicsUC Berkeley1626 Russell StBerkeley, CA 94703, USAemail: kevin@math.berkeley.edu

Michael LonneMathematikUniversitat BayreuthUniversitatsstrasse 30Bayreuth, 95444, Germanyemail:Michael.Loenne@uni-bayreuth.de

Santiago Lopez de MedranoInstituto de MatematicasUniversidad Nacional Autonoma deMexicoCiudad Unversitaria, Circuito Exterior04510, Mexicoemail: santiago@matem.unam.mx

Marıa Teresa Lozano ImızcozMatematicasUniversidad de ZaragozaC/ Pedro Cerbuna, 12Zaragoza, 50009, Spainemail: tlozano@unizar.es

Ursula LudwigMathematisches InstitutUniversitat FreiburgEckerstrasse 1Freiburg, 79104, Germanyemail:ursula.ludwig@math.uni-freiburg.de

Ignacio Luengo VelascoAlgebraUniversidad Complutense de MadridPlaza de las Ciencias 3Madrid, 28040, Spainemail: iluengo@mat.ucm.es

Miguel Angel Marco-BuzunarizICMATConsejo Superior de InvestigacionesCientıficasPlaza de las ciencias 3Madrid, 28040, Spainemail: mmarco@unizar.es

Jorge Martın-MoralesMatematicasUniversidad de ZaragozaC/Pedro Cerbuna 12Zaragoza, 50009, Spainemail: jorge@unizar.es

Daniel MateiGeometry and TopologyIMARP.O. BOX 1-764Bucharest, RO-014700, ROMANIAemail: daniel.matei@imar.ro

Laurentiu George MaximMathematics and Computer ScienceCUNY, Lehman College250 Bedford Park Blvd West, GilletHall 100Bronx, NY 10468, USAemail:laurentiu.maxim@lehman.cuny.edu

Lee J McEwanMathematicsOhio State University - Mansfield316 Chambers Rd.Mansfield, OH 44903, USAemail: mcewan@math.ohio-state.edu

Alejandro Melle HernandezAlgebraUniversidad ComplutensePlaza de las Ciencias 3Madrid, 28040, Spainemail: amelle@mat.ucm.es

xx PARTICIPANTS

Aurelio MenegonInstituto de MatematicasUNAMAv. UniversidadCuernavaca, 62215, Mexicoemail: aurelio@matcuer.unam.mx

Malgorzata MikoszFaculty of Mathematics andInformation ScienceWarsaw University of TechnologyPlac Politechniki 1Warsaw, 00-661, Polandemail:emmikosz@adam.mech.pw.edu.pl

Jose Marıa Montesinos AmilibiaMatematicasUCMPlaza de Ciencias, 3Madrid, 28040, Espanaemail: montesin@mat.ucm.es

Juan Antonio Moya PerezGeometria y TopologiaUniversitat de ValenciaSanta Teresa n.67Valencia, 46110, Spainemail: mojuanan@alumni.uv.es

Mircea MustataMathematicsUniversity of Michigan530 Church Street, East HalAnn Arbor, MI 48109, USAemail: mmustata@umich.edu

Luis Narvaez MacarroAlgebraUniversidad de SevillaAvda, Reina Mercedes, s/nSevilla, 41012, Spainemail: narvaez@algebra.us.es

Andras NemethiGeometryRenyi Institute of MathematicsRealtanoda utca 13-15Budapest, H-1053, Hungaryemail: nemethi@renyi.hu

Walter D NeumannMathematicsBarnard College, Columbia University2990 Broadway MC4424New York, NY 10027, USAemail: neumann@math.columbia.edu

Juan Jose Nuno-BallesterosGeometria i TopologiaUniversitat de ValenciaC/Dr. Moliner, 50Burjassot, 46100, Spainemail: Juan.Nuno@uv.es

Donal O’SheaMathematicsMount Holyoke College50 College StSouth Hadley, MA 01075, USAemail: doshea@mtholyoke.edu

Mutsuo OkaMathematicsTokyo University of ScienceWakamiya 26, Shinjuku-kuTokyo, 1620827, Japanemail: oka@rs.kagu.tus.ac.jp

Robert Olivares MoralesMathematical Physics and GeometryUniversity of Paris VI/StanfordUniversity4, place de JussieuParis, 75005, Franceemail: olivaresmorales@imel.org

PARTICIPANTS xxi

Stepan OrevkovUFR MIGIMT, Universite Paul Sabatier,118 route de NarbonneToulouse, 31062, Franceemail: orevkov@math.ups-tlse.fr

Jorge Ortigas GalindoMatematicasUniversidad de ZaragozaC/ Pedro Cerbuna 12Zaragoza, 50009, Spainemail: jorge ortigas@hotmail.com

Raul Oset SinhaGeometria i TopologiaUniversitat de Valenciac/Vicent Andres Estelles s.n.Burjassot, Valencia, 46100, Spainemail: raul.oset@uv.es

Ferit OzturkMathematicsBogazici UniversityBebekIstanbul, 34342, Turkeyemail: ferit.ozturk@boun.edu.tr

Luis ParisIMB, UMR 5584 du CNRSUniversite de BourgogneB.P. 47870Dijon, 21078, Franceemail: lparis@u-bourgogne.fr

Marıa Pe PereiraAlgebraUniversidad Complutense de MadridPlza de Ciencias 3Madrid, 28040, Spainemail: maria.pe@mat.ucm.es

Tuan PhamMathematicsUniversity of Illinois at Chicago1030 South May Street, Apartment 3Chicago, IL 60607, USAemail: anhtuan@math.uic.edu

Anne PichonInstitut de Mathematiques de LuminyUniversite de la Mediterranee163 av. de Luminy case 907,Marseille, 13288, Franceemail: pichon@iml.univ-mrs.fr

Francesco PolizziMathematicsUniversita della CalabriaVia P. Bucci Cubo 30 BArcavacata di Rende - Cosenza, 87036,Italyemail: polizzi@mat.unical.it

Patrick Popescu-PampuInst. Math. de JussieuUniv. Paris 7 Diderot175, rue du ChevaleretParis, 75013, Franceemail: ppopescu@math.jussieu.fr

Richard RandellMathematicsUniversity of IowaMacLean Hall, room 1CIowa City, Iowa 52245, USAemail: randell@math.uiowa.edu

Ana RegueraDepartamento de Algebra y GeometrıaUniversidad de ValladolidC. Prado de la Magdalena snValladolid, 47005, spainemail: areguera@agt.uva.es

xxii PARTICIPANTS

Fernando RomanAlgebraUniversidad Complutense de MadridArriazaMadrid, 28008, Spainemail: ferchu@mat.ucm.es

Consuelo RoyCultural CommitteeZaragoza, Spainemail: consueloroy@hotmail.com

Marcelo Jose SaiaMathematicsInstituto de Ciencias Matematicas edeComputacaoRua Sao Joao Bosco, 436, PlanaltoParaisoSao Carlos, Sao Paulo 13562090, Brazilemail: mjsaia@icmc.usp.br

Nermin Salepci FerretDept. of MathematicsKoc UniversityRumeli Feneri yoluIstanbul, 34450, Turkeyemail: nferret@ku.edu.tr

Mario SalvettiDipartimento di Matematica ”L.Tonelli”Universita di PisaLargo Pontecorvo, 5Pisa, 56127, Italyemail: salvetti@dm.unipi.it

Guillermo Penafort SanchısGeometrıa y topologıaUniversitat de ValenciaCarniceros 20Valencia, Valencia 46001, Espanaemail: guillermo.penafort@uv.es

Jean Venato SantosMathematicsICMC - USPMora de Rubielos, n. 14 Piso: 2, 9Valencia, Valencia 46007, Espanaemail: jvenatos@icmc.usp.br

Jan SchepersDepartment of MathematicsUniversity of LeuvenCelestijnenlaan 200BHeverlee, 3001, Belgiumemail: janschepers1@gmail.com

Inna ScherbakSchool of Mathematical SciencesTel Aviv UniversityHaim Lavnon streetTel Aviv, 69978, Israelemail: scherbak@post.tau.ac.il

Jose Antonio SeadeInstituto de MatematicasUniversidad Nacional Autonoma deMexicoAv. Universidad s/n, Lomas deChamilpCuernavaca, 62210, Mexicoemail: jseade@matcuer.unam.mx

Mamuka ShubladzeMathematicsTbilisi State UniversityChavchavadze av.1Tbilisi, 0128, Georgiaemail: mamushubladze@yahoo.com

Dirk SiersmaDepartment of MathematicsUtrecht UniversityBudapestlaan 6Utrecht, 3508TA, The Netherlandsemail: D.Siersma@uu.nl

PARTICIPANTS xxiii

Marcela SilvaICMC - Instituto de CienciasMatematicas e de ComputacaoUniversidade de Sao PauloAv. Trabalhador Sao-carlense, 400 -CentroSao Carlos, 13560-970, Brasilemail: masilva@icmc.usp.br

Jawad SnoussiInstituto de Matematicas UnidadCuernavacaUniversidad Nacional Autonoma deMexicoAv. Universidad S/N, Lomas deChamilpaCuernavaca, Morelos, 62250, Mexicoemail: jsnoussi@matcuer.unam.mx

Pere Soto TejedorCultural CoordinatorBarcelona, Spainemail: peresoto@peresoto.com

Steven SperbermathematicsUniversity of Minnesota127 Vincent Hall Church StreetMinneapolis, MN 55455, USAemail: sperber@math.umn.edu

Alexander I. SuciuMathematicsNortheastern University360 Huntington AvenueBoston, MA 02115, USAemail: a.suciu@neu.edu

Mina TeicherEmmy Noether InstituteBarIlan UniversityKeren HayesodRamat Gan, 52900, Israelemail: teicher@macs.biu.ac.il

Domingo ToledoMathematicsUniversity of Utah155 South 1400 EastSalt Lake City, UT 84112-0090, UnitedStatesemail: toledo@math.utah.edu

Meral TosunMathematicsGalatasaray UniversityCiragan cd. No 36 OrtakoyIstanbul, 34357, Turkiyeemail: mtosun@gsu.edu.tr

Vıctor Tovıo CiercolesDepartamento de MatematicasUniversidad de Zaragozac/ Cerbuna, 12Zaragoza, 50009, Espanaemail: tovio@unizar.es

Ilya TyomkinMathematicsBen Gurion UniversityP.O.B. 653Beer Sheva, 84105, Israelemail: tyomkin@cs.bgu.ac.il

Aaron David ValdiviaMathematicsFlorida State University1534A Yancey StTallahassee, FL 32303, USAemail: avaldivi@math.fsu.edu

Jean VallesLaboratoire de MathematiquesUniversite de PauAvenue de l’universitePau, 64000, Franceemail: jean.valles@univ-pau.fr

xxiv PARTICIPANTS

Willem VeysWiskundeK.U.LeuvenCelestijnenlaan 200BLeuven, 3001, Belgiumemail: wim.veys@wis.kuleuven.be

Florens VincentLMAUniversite de Pau et des pays del’AdourAv. de l’universite, BP 576Pau, 64012, Franceemail: vincent.florens@univ-pau.fr

Robert Edward WaelderMathematicsUniversity of Illinois at Chicago851 S Morgan StChicago, IL 60607, United Statesemail: rwaelder@math.uic.edu

Philip WagreichMathematics, Statistics, and ComputerScience/Learning ScienUniversity of Illinois at Chicago925 Fair Oaks AvenueOak Park, IL 60302, USAemail: wagreich@uic.edu

Jonathan WahlMathematicsUniversity of North CarolinaUNC-Chapel HillChapel Hill, NC 27599-3250, USAemail: jmwahl@email.unc.edu

Botong WangMathPurdue University150 N. University StreetWest Lafayette, IN 47907, USemail: wang191@math.purdue.edu

Andrzej WeberInstitute of MathematicsUniversity of Warsawul Banacha 2Warszawa, 02-097, Polandemail: aweber@mimuw.edu.pl

John W. WoodMathematics M/C 249Univ of Illinois at Chicago851 S. Morgan StreetChicago, IL 60607, USAemail: jwood@math.uic.edu

Fei YeMathematics, Statistics, and ComputerScienceUniversity of Illinois at Chicago851 S. Morgan StreetChicago, Illinois 60607, USAemail: fye@math.uic.edu

Elif YilmazMathematicsMiddle East Technical UniversityMutlukoy Sitesi 9.sokak No 1, UmitkoyAnkara, 906530, Turkeyemail: elyilmaz@metu.edu.tr

Sergey YuzvinskyMathematicsUniversity of Oregon13th ave.Eugene, Oregon 97405, USAemail: yuz@uoregon.edu

Michelle Ferreira ZanchettaMathematicsICMC-USPOrlando Damiano, 1961Sao Carlos, Sao Paulo13560-450, Brasilemail: ferreira@icmc.usp.br

Titles in This Series

540 Denis Bonheure, Mabel Cuesta, Enrique J. Lami Dozo, Peter Takac, Jean VanSchaftingen, and Michel Willem, Editors, Nonlinear Elliptic Partial DifferentialEquations, 2011

539 Kurusch Ebrahimi-Fard, Matilde Marcolli, and Walter D. van Suijlekom,Editors, Combinatorics and Physics, 2011

538 Jose Ignacio Cogolludo-Agustın and Eriko Hironaka, Editors, Topology ofalgebraic varieties and singularities, 2011

537 Cesar Polcino Milies, Editor, Groups, algebras and applications, 2011

536 Kazem Mahdavi, Debbie Koslover, and Leonard L. Brown III, Editors, Crossdisciplinary advances in quantum computing, 2011

535 Maxim Braverman, Leonid Friedlander, Thomas Kappeler, Peter Kuchment,Peter Topalov, and Jonathan Weitsman, Editors, Spectral theory and geometricanalysis, 2011

534 Pere Ara, Fernando Lledo, and Francesc Perera, Editors, Aspects of operatoralgebras and applications, 2011

533 L. Babinkostova, A. E. Caicedo, S. Geschke, and M. Scheepers, Editors, Settheory and its applications, 2011

532 Sergiy Kolyada, Yuri Manin, Martin Moller, Pieter Moree, and Thomas Ward,Editors, Dynamical numbers: Interplay between dynamical systems and number theory,2010

531 Richard A. Brualdi, Samad Hedayat, Hadi Kharaghani, Gholamreza B.Khosrovshahi, and Shahriar Shahriari, Editors, Combinatorics and graphs, 2010

530 Vitaly Bergelson, Andreas Blass, Mauro Di Nasso, and Renling Jin, Editors,Ultrafilters across Mathematics, 2010

529 Robert Sims and Daniel Ueltschi, Editors, Entropy and the Quantum, 2010

528 Alberto Farina and Enrico Valdinoci, Editors, Symmetry for Elliptic PDEs, 2010

527 Ricardo Castano-Bernard, Yan Soibelman, and Ilia Zharkov, Editors, Mirrorsymmetry and tropical geometry, 2010

526 Helge Holden and Kenneth H. Karlsen, Editors, Nonlinear partial differentialequations and hyperbolic wave phenomena, 2010

525 Manuel D. Contreras and Santiago Dıaz-Madrigal, Editors, Five lectures incomplex analysis, 2010

524 Mark L. Lewis, Gabriel Navarro, Donald S. Passman, and Thomas R. Wolf,Editors, Character theory of finite groups, 2010

523 Aiden A. Bruen and David L. Wehlau, Editors, Error-correcting codes, finitegeometries and cryptography, 2010

522 Oscar Garcıa-Prada, Peter E. Newstead, Luis Alverez-Consul, Indranil Biswas,Steven B. Bradlow, and Tomas L. Gomez, Editors, Vector bundles and complexgeometry, 2010

521 David Kohel and Robert Rolland, Editors, Arithmetic, geometry, cryptography andcoding theory 2009, 2010

520 Manuel E. Lladser, Robert S. Maier, Marni Mishna, and Andrew Rechnitzer,Editors, Algorithmic probability and combinatorics, 2010

519 Yves Felix, Gregory Lupton, and Samuel B. Smith, Editors, Homotopy theory offunction spaces and related topics, 2010

518 Gary McGuire, Gary L. Mullen, Daniel Panario, and Igor E. Shparlinski,Editors, Finite fields: Theory and applications, 2010

517 Tewodros Amdeberhan, Luis A. Medina, and Victor H. Moll, Editors, Gems inexperimental mathematics, 2010

516 Marlos A.G. Viana and Henry P. Wynn, Editors, Algebraic methods in statisticsand probability II, 2010

515 Santiago Carrillo Menendez and Jose Luis Fernandez Perez, Editors,Mathematics in finance, 2010

TITLES IN THIS SERIES

514 Arie Leizarowitz, Boris S. Mordukhovich, Itai Shafrir, and Alexander J.Zaslavski, Editors, Nonlinear analysis and optimization II, 2010

513 Arie Leizarowitz, Boris S. Mordukhovich, Itai Shafrir, and Alexander J.Zaslavski, Editors, Nonlinear analysis and optimization I, 2010

512 Albert Fathi, Yong-Geun Oh, and Claude Viterbo, Editors, Symplectic topologyand measure preserving dynamical systems, 2010

511 Luise-Charlotte Kappe, Arturo Magidin, and Robert Fitzgerald Morse, Editors,Computational group theory and the theory of groups, II, 2010

510 Mario Bonk, Jane Gilman, Howard Masur, Yair Minsky, and Michael Wolf,Editors, In the Tradition of Ahlfors-Bers, V, 2010

509 Primitivo B. Acosta-Humanez and Francisco Marcellan, Editors, Differentialalgebra, complex analysis and orthogonal polynomials, 2010

508 Martin Berz and Khodr Shamseddine, Editors, Advances in p-Adic andnon-archimedean analysis, 2010

507 Jorge Arvesu, Francisco Marcellan, and Andrei Martınez-Finkelshtein, Editors,Recent trends in orthogonal polynomials and approximation theory, 2010

506 Yun Gao, Naihuan Jing, Michael Lau, and Kailash C. Misra, Editors, Quantumaffine algebras, extended affine Lie algebras, and their applications, 2010

505 Patricio Cifuentes, Jose Garcıa-Cuerva, Gustavo Garrigos, Eugenio Hernandez,Jose Marıa Martell, Javier Parcet, Alberto Ruiz, Fernando Soria, Jose LuisTorrea, and Ana Vargas, Editors, Harmonic analysis and partial differential equations,2010

504 Christian Ausoni, Kathryn Hess, and Jerome Scherer, Editors, Alpineperspectives on algebraic topology, 2009

503 Marcel de Jeu, Sergei Silvestrov, Christian Skau, and Jun Tomiyama, Editors,Operator structures and dynamical systems, 2009

502 Viviana Ene and Ezra Miller, Editors, Combinatorial Aspects of CommutativeAlgebra, 2009

501 Karel Dekimpe, Paul Igodt, and Alain Valette, Editors, Discrete groups andgeometric structures, 2009

500 Philippe Briet, Francois Germinet, and Georgi Raikov, Editors, Spectral andscattering theory for quantum magnetic systems, 2009

499 Antonio Giambruno, Cesar Polcino Milies, and Sudarshan K. Sehgal, Editors,Groups, rings and group rings, 2009

498 Nicolau C. Saldanha, Lawrence Conlon, Remi Langevin, Takashi Tsuboi,

and Pawel Walczak, Editors, Foliations, geometry and topology, 2009

497 Maarten Bergvelt, Gaywalee Yamskulna, and Wenhua Zhao, Editors, Vertexoperator algebras and related areas, 2009

496 Daniel J. Bates, GianMario Besana, Sandra Di Rocco, and Charles W.Wampler, Editors, Interactions of classical and numerical algebraic geometry, 2009

495 G. L. Litvinov and S. N. Sergeev, Editors, Tropical and idempotent mathematics,2009

494 Habib Ammari and Hyeonbae Kang, Editors, Imaging microstructures:Mathematical and computational challenges, 2009

493 Ricardo Baeza, Wai Kiu Chan, Detlev W. Hoffmann, and Rainer Schulze-Pillot,Editors, Quadratic Forms—Algebra, Arithmetic, and Geometry, 2009

492 Fernando Giraldez and Miguel A. Herrero, Editors, Mathematics, DevelopmentalBiology and Tumour Growth, 2009

491 Carolyn S. Gordon, Juan Tirao, Jorge A. Vargas, and Joseph A. Wolf, Editors,New developments in Lie theory and geometry, 2009

For a complete list of titles in this series, visit theAMS Bookstore at www.ams.org/bookstore/.

CONM/538

This volume contains invited expository and research papers from the conference Topology of Algebraic Varieties, in honor of Anatoly Libgober’s 60th birthday, held June 22–26, 2009, in Jaca, Spain.

The volume contains four parts corresponding to the four main focal points of the confer-ence: algebraic geometry and fundamental groups, braids and knots, hyperplane arrange-ments, and singularities. Together, the papers provide an overview of the current status of a broad range of topological questions in Algebraic Geometry.

American Mathematical Societywww.ams.org

Real Sociedad Matemática Españolawww.rsme.es