C ONTEMPORARY M ATHEMATICS 474 Singularities I Algebraic and Analytic Aspects International Conference in Honor of the 60th Birthday of Lê Du˜ng Tráng January 8–26, 2007 Cuernavaca, Mexico Jean-Paul Brasselet José Luis Cisneros-Molina David Massey José Seade Bernard Teissier Editors American Mathematical Society This page intentionally left blank Singularities I Algebraic and Analytic Aspects This page intentionally left blank C ONTEMPORARY M ATHEMATICS 474 Singularities I Algebraic and Analytic Aspects International Conference in Honor of the 60th Birthday of Lê Du˜ng Tráng January 8–26, 2007 Cuernavaca, Mexico Jean-Paul Brasselet José Luis Cisneros-Molina David Massey José Seade Bernard Teissier Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeTurck, managing editor George Andrews Abel Klein Martin J. Strauss 2000 Mathematics Subject Classification. Primary14B05, 14E15,14J17, 32Sxx, 34M35, 35A20. Library of Congress Cataloging-in-Publication Data Singularities : international conference in honor of the 60th birthday of Lˆe Du˜ng Tr´ang, January8–26,2007,Cuernavaca,Mexico/Jean-PaulBrasselet...[etal.],editors. v.cm. —(Contemporarymathematics;v.474–475) Includesbibliographicalreferences. Contents: 1.Algebraicandanalyticaspects—2.Geometricandtopologicalaspects. ISBN978-0-8218-4458-8(v.1: alk.paper)—ISBN978-0-8218-4717-6(v.2: alk.paper) 1.Singularities(Mathematics)—Congresses. I.Tr´ang,LˆeDu˜ng. II.Brasselet,Jean-Paul. QA614.58.S5556 2008 516.3(cid:1)5—dc22 2008028179 Copying and reprinting. Materialinthis bookmaybe reproducedby anymeansforedu- cationaland scientific purposes without fee or permissionwith the exception of reproduction by servicesthatcollectfeesfordeliveryofdocumentsandprovidedthatthecustomaryacknowledg- ment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercialuseofmaterialshouldbeaddressedtotheAcquisitionsDepartment,AmericanMath- ematical Society, 201 Charles Street, Providence, Rhode Island 02904-2294, USA. Requests can [email protected]. Excludedfromtheseprovisionsismaterialinarticlesforwhichtheauthorholdscopyright. In suchcases,requestsforpermissiontouseorreprintshouldbeaddresseddirectlytotheauthor(s). (Copyrightownershipisindicatedinthenoticeinthelowerright-handcornerofthefirstpageof eacharticle.) (cid:1)c 2008bytheAmericanMathematicalSociety. Allrightsreserved. TheAmericanMathematicalSocietyretainsallrights exceptthosegrantedtotheUnitedStatesGovernment. Copyrightofindividualarticlesmayreverttothepublicdomain28years afterpublication. ContacttheAMSforcopyrightstatusofindividualarticles. PrintedintheUnitedStatesofAmerica. (cid:1)∞ Thepaperusedinthisbookisacid-freeandfallswithintheguidelines establishedtoensurepermanenceanddurability. VisittheAMShomepageathttp://www.ams.org/ 10987654321 131211100908 To Lˆe Du˜ng Tra´ng in celebration of his first 60 years. This page intentionally left blank Contents Preface ix List of Participants xi On the Log-Canonical Threshold for Germs of Plane Curves E. Artal Bartolo, Pi. Cassou-Nogu`es, I. Luengo, and A. Melle-Herna´ndez 1 Intersection Cohomology Invariants of Complex Algebraic Varieties S. E. Cappell, L. Maxim, and J. L. Shaneson 15 Topology of Algebraic Morphisms F. El Zein 25 Non-isolated Complete Intersection Singularities and the A Condition f T. Gaffney 85 Unique Range Sets and Decomposition of Meromorphic Functions H. H. Khoai 95 Enriched Relative Polar Curves and Discriminants D. B. Massey 107 Hodge-Theoretic Atiyah-Meyer Formulae and the Stratified Multiplicative Property L. Maxim and J. Schu¨rmann 145 Vertical Monodromy and Spectrum of a Yomdin Series L. J. McEwan 167 Structures de Frobenius et Exposants de la Monodromie p-adique des E´quations Diff´erentielles Z. Mebkhout 175 Linearity Conditions on the Jacobian Ideal and Logarithmic–Meromorphic Comparison for Free Divisors L. N. Macarro 245 Poincar´e Series Associated with Surface Singularities A. N´emethi 271 Approximation de Artin Cylindrique et Morphismes d’Alg`ebres Analytiques G. Rond 299 vii viii CONTENTS An Explicit Stationary Phase Formula for the Local Formal Fourier-Laplace Transform C. Sabbah 309 On Modified C(cid:1)-Trivialization of C(cid:1)+1-Real Germs of Functions M. J. Saia and C. H. Soares Jr. 331