Singularities: The Brieskorn Anniversary Volume

ISBN-13: 9783034897679 / Angielski / Miękka / 2012 / 488 str.

Vladimir I. Arnold; Gert-Martin Greuel; Joseph H. M. Steenbrink

Opis

In July 1996, a conference was organized by the editors of this volume at the Mathematische Forschungsinstitut Oberwolfach to honour Egbert Brieskorn on the occasion of his 60th birthday. Most of the mathematicians invited to the conference have been influenced in one way or another by Brieskorn's work in singularity theory. It was the first time that so many people from the Russian school could be present at a conference in singularity theory outside Russia. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrating the breadth of Brieskorn's own interests. This volume contains papers on singularity theory and its applications, written by participants of the conference. In many cases, they are extended versions of the talks presented there. The diversity of subjects of the contributions reflects singularity theory's relevance to topology, analysis and geometry, combining ideas and techniques from all of these fields, as well as demonstrates the breadth of Brieskorn's own interests.

Spis treści

1: Classification and Invariants.- On Schappert’s Characterization of Strictly Unimodal Plane Curve Singularities.- Geometric Quotients of Unipotent Group Actions II.- Hodge Numbers for Isolated Singularities of Non-degenerate Complete Intersections.- Differential Invariants of Embeddings of Manifolds in Complex Spaces.- On the Spectrum of Curve Singularities.- Embedding Nonisolated Singularities into Isolated Singularities.- 2: Deformation Theory.- Discriminants and Vector Fields.- Suspensions of Fat Points and Their Intersection Forms.- Brieskorn Lattices and Torelli Type Theorems for Cubics in ?3 and for Brieskorn-Pham Singularities with Coprime Exponents.- Equiclassical Deformation of Plane Algebraic Curves.- Monodromy of Complete Intersections and Surface Potentials.- 3: Resolution.- P-Resolutions of Cyclic Quotients from the Toric Viewpoint.- On Characteristic Cones, Clusters and Chains of Infinitely Near Points.- On Kleinian Singularities and Quivers.- Seventeen Obstacles for Resolution of Singularities.- 4: Applications.- Sur la topologie des polynômes complexes.- Five Definitions of Critical Point at Infinity.- Evaluation of Fermion Loops by Iterated Residues.- Möbius and Odd Real Trigonometric M-Functions.- Moduli Space of Smooth Affine Curves of a Given Genus with one Place at Infinity.- Shadows of Legendrian Links and J+-Theory of Curves.