New Developments in Singularity Theory

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 Parusiński

      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

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.

• Meromorphic function
• Monodromy
• Tensor
• manifold
• singularity theory

• 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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