**Contemporary Mathematics**

Volume: 538;
2011;
467 pp;
Softcover

MSC: Primary 00; 14; 32; 57; 51; 53; 55;

**Print ISBN: 978-0-8218-4890-6
Product Code: CONM/538**

List Price: $135.00

AMS Member Price: $108.00

MAA Member Price: $121.50

**Electronic ISBN: 978-0-8218-8217-7
Product Code: CONM/538.E**

List Price: $135.00

AMS Member Price: $108.00

MAA Member Price: $121.50

# Topology of Algebraic Varieties and Singularities

Share this page *Edited by *
*José Ignacio Cogolludo-Agustín; Eriko Hironaka*

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 conference: algebraic geometry and fundamental groups, braids and
knots, hyperplane arrangements, and singularities. Together, the papers
provide an overview of the current status of a broad range of topological
questions in Algebraic Geometry.

This book is published in cooperation with Real Sociedad Matemática Española (RSME)

#### Readership

Graduate students and research mathematicians interested in algebraic geometry and fundamental groups, braids and knots, hyperplane arrangements, and singularity theory.

# Table of Contents

## Topology of Algebraic Varieties and Singularities

- Contents vii8 free
- Preface ix10 free
- List of Participants xiii14 free
- Part I: A Historical Note 126 free
- Part II: Algebraic Geometry and Fundamental Groups 1944
- Feynman Motives and Deletion-Contraction Relations 2146
- Classification of Fundamental Groups of Galois Covers of Surfaces of Small Degree Degenerating to Nice Plane Arrangements 6590
- Homomorphisms between Kähler groups 95120
- Quasi-Projectivity, Artin-Tits Groups, and Pencil Maps 113138
- Topology of Plane Algebraic Curves: The Algebraic Approach 137162
- Hirzebruch Invariants of Symmetric Products 163188
- Fundamental Groups, Alexander Invariants, and Cohomology Jumping Loci 179204
- 1. Introduction 180205
- 2. Characteristic varieties 183208
- 3. Homology of abelian covers 186211
- 4. Alexander invariants 188213
- 5. Resonance varieties 192217
- 6. Bieri–Neumann–Strebel–Renz invariants 195220
- 7. Formality properties 197222
- 8. Kähler and quasi-Kähler manifolds 199224
- 9. Hyperplane arrangements 204229
- 10. Milnor fibrations 211236
- 11. Three-dimensional manifolds 215240
- References 219244

- Part III: Braids and Knots 225250
- Part IV: Hyperplane Arrangements 277302
- Part V: Singularities 319344
- On ν-Quasi-Ordinary Power Series: Factorization, Newton Trees and Resultants 321346
- Milnor Fibrations for Real and Complex Singularities 345370
- On Homotopy Types of Complements of Analytic Sets and Milnor Fibres 363388
- The Milnor Fiber Signature is not Semicontinuous 369394
- Principal Analytic Link Theory in Homology Sphere Links 377402
- On Mixed Brieskorn Variety 389414
- Introduction to Jung's Method of Resolution of Singularities 401426
- Biggest Sharp Polynomial Estimate of Integral Points in Right-Angled Simplices 433458