edited by Jean-Paul Brasselet (Institut de Mathématiques de Luminy-CNRS, France) , James Damon (University of North Carolina, USA) , Lê Dũng Tráng (ICTP, Trieste, Italy) , & Mutsuo Oka (Tokyo University of Science, Japan)

Table of Contents (76k)
Chapter 1: Introduction to Basic Toric Geometry (1,132k)

Singularity theory appears in numerous branches of mathematics, as well as in many emerging areas such as robotics, control theory, imaging, and various evolving areas in physics. The purpose of this proceedings volume is to cover recent developments in singularity theory and to introduce young researchers from developing countries to singularities in geometry and topology.

The contributions discuss singularities in both complex and real geometry. As such, they provide a natural continuation of the previous school on singularities held at ICTP (1991), which is recognized as having had a major influence in the field.

• Introduction to Basic Toric Geometry (G Barthel et al.)
• Poincaré-Hopf Theorems on Singular Varieties (J-P Brasselet)
• On Milnor's Fibration Theorem for Real and Complex Singularities (J Seade)
• Metric Theory of Singularities. Lipschitz Geometry of Singular Spaces (L Birbrair)
• Lectures on Monodromy (W Ebeling & S M Gusein-Zade)
• Computational Aspects of Singularities (A Frühbis-Krüger)
• Lagrangian and Legendrian Varieties and Stability of Their Projections (V V Goryunov & V M Zakalyukin)
• Problems in Topology of the Complement to Plane Singular Curves (A Libgober)
• Topology of Degeneration of Riemann Surfaces (Y Matsumoto)
• Graded Roots and Singularities (A Némethi)
• Chern Classes and Thom Polynomials (T Ohmoto)
• McKay Correspondence for Quotient Surface Singularities (O Riemenschneider)
• A Lefschetz Theorem on the Picard Group of Complex Projective Varieties (H A Hamm & D T Lê)
• Tangential Alexander Polynomials and Non-reduced Degeneration (M Oka)
• Logarithmic Vector Fields and Multiplication Table (S Tanabé)
• and other papers