Trends in Singularities

1. Front Matter

   Pages i-ix

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2. On Sextic Curves with Big Milnor Number

   • Enrique Artal Bartolo, Jorge Carmona Ruber, José Ignacio Cogolludo Agustín

   Pages 1-29

3. Résolution des Singularités de Surfaces par Éclatements Normalisés

   • Romain Bondil, Dũng Tráng Lê

   Pages 31-81

4. Sectional Singularities and Geometry of Families of Planar Quadratic Forms

   • J. W. Bruce, V. V. Goryunov, V. M. Zakalyukin

   Pages 83-97

5. On the Cohomology of Fibres of Polynomial Maps

   • Helmut A. Hamm

   Pages 99-113

6. Generic Torelli for Semiquasihomogeneous Singularities

   • Claus Hertling

   Pages 115-140

7. Eigenvalues for the Monodromy of the Milnor Fibers of Arrangements

   • Anatoly Libgober

   Pages 141-150

8. Fundamental Group of Sextics of Torus Type

   • Mutsuo Oka, Duc Tai Pho

   Pages 151-180

9. Universal Abelian Covers of Surface Singularities

   • Walter D. Neumann, Jonathan Wahl

   Pages 181-190

10. On Real Singularities with a Milnor Fibration

    • Maria Aparecida Soares Ruas, José Seade, Alberto Verjovsky

    Pages 191-213

11. Braid Monodromy Type Invariants of Surfaces and 4-Manifolds

    • Mina Teicher

    Pages 215-222

12. Singularities and Topology of Meromorphic Functions

    • Mihai Tibăr

    Pages 223-246

The collection of papers in this volume represents recent advances in the under­ standing of the geometry and topology of singularities. The book covers a broad range of topics which are in the focus of contemporary singularity theory. Its idea emerged during two Singularities workshops held at the University of Lille (USTL) in 1999 and 2000. Due to the breadth of singularity theory, a single volume can hardly give the complete picture of today's progress. Nevertheless, this collection of papers provides a good snapshot of what is the state of affairs in the field, at the turn of the century. Several papers deal with global aspects of singularity theory. Classification of fam­ ilies of plane curves with prescribed singularities were among the first problems in algebraic geometry. Classification of plane cubics was known to Newton and classification of quartics was achieved by Klein at the end of the 19th century. The problem of classification of curves of higher degrees was addressed in numerous works after that. In the paper by Artal, Carmona and Cogolludo, the authors de­ scribe irreducible sextic curves having a singular point of type An (n > 15) and a large (Le. , :::: 18) sum of Milnor numbers of other singularities. They have discov­ ered many interesting properties of these families. In particular they have found new examples of so-called Zariski pairs, i. e.

• Algebraic geometry
• Fundamental group
• cohomology
• homology
• singularity theory
• topology

• Department of Mathematics, University of Illinois at Chicago, Chicago, USA

  Anatoly Libgober

• Mathématiques, UMR-CNRS 8524, Villeneueve d’Ascq Cedex, France

  Mihai Tibăr

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