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New Developments in Singularity Theory

  • Book
  • © 2001

Overview

Editors:
  1. D. Siersma

    1. Department of Mathematics, University Utrecht, Utrecht, The Netherlands

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  2. C. T. C. Wall

    1. Mathematical Sciences, Liverpool, UK

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    You can also search for this editor in PubMed   Google Scholar

  3. V. Zakalyukin

    1. Moscow Aviation Institute, Moscow, Russian Republic

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    You can also search for this editor in PubMed   Google Scholar

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry (NAII, volume 21)

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Table of contents (18 chapters)

  1. Front Matter

    Pages i-viii
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  2. Singularities of real maps

    1. Front Matter

      Pages 1-1
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    2. Classifications in Singularity Theory and Their Applications

      • James William Bruce
      Pages 3-33

    3. Applications of Flag Contact Singularities

      • Vladimir Zakalyukin
      Pages 35-64

    4. On Stokes Sets

      • Yuliy Baryshnikov
      Pages 65-86

    5. Resolutions of discriminants and topology of their complements

      • Victor Vassiliev
      Pages 87-115

    6. Classifying Spaces of Singularities and Thom Polynomials

      • Maxim Kazarian
      Pages 117-134

    7. Singularities and Noncommutative Geometry

      • Jean-Paul Brasselet
      Pages 135-155

  3. Singular complex varietes

    1. Front Matter

      Pages 157-157
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    2. The Geometry of Families of Singular Curves

      • Gert-Martin Greuel, Christoph Lossen
      Pages 159-192

    3. On the preparation theorem for subanalytic functions

      • Adam ParusiÅ„ski
      Pages 193-215

    4. Computing Hodge-theoretic invariants of singularities

      • Mathias Schulze, Joseph Steenbrink
      Pages 217-233

    5. Frobenius manifolds and variance of the spectral numbers

      • Claus Hertling
      Pages 235-255

    6. Monodromy and Hodge Theory of Regular Functions

      • Alexandru Dimca
      Pages 257-278

    7. Bifurcations and topology of meromorphic germs

      • Sabir Gusein-Zade, Ignacio Luengo, Alejandro Melle Hernández
      Pages 279-304

    8. Unitary reflection groups and automorphisms of simple hypersurface singularities

      • Victor V. Goryunov
      Pages 305-328

    9. Simple Singularities and Complex Reflections

      • Peter Slodowy
      Pages 329-348

  4. Singularities of holomorphic maps

    1. Front Matter

      Pages 349-349
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    2. Discriminants, vector fields and singular hypersurfaces

      • Andrew A. du Plessis, C. T. C. Wall
      Pages 351-377

    3. The theory of integral closure of ideals and modules: Applications and new developments

      • Terence Gaffney
      Pages 379-404
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Keywords

About this book

Singularities arise naturally in a huge number of different areas of mathematics and science. As a consequence, singularity theory lies at the crossroads of paths that connect many of the most important areas of applications of mathematics with some of its most abstract regions.
The main goal in most problems of singularity theory is to understand the dependence of some objects of analysis, geometry, physics, or other science (functions, varieties, mappings, vector or tensor fields, differential equations, models, etc.) on parameters.
The articles collected here can be grouped under three headings. (A) Singularities of real maps; (B) Singular complex variables; and (C) Singularities of homomorphic maps.

Editors and Affiliations

  • Department of Mathematics, University Utrecht, Utrecht, The Netherlands

    D. Siersma

  • Mathematical Sciences, Liverpool, UK

    C. T. C. Wall

  • Moscow Aviation Institute, Moscow, Russian Republic

    V. Zakalyukin

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