New Developments in Singularity Theory

2001. Auflage 2001
ISBN: 978-0-7923-6996-7
Verlag: Springer

Buch, Englisch, Band 21, 472 Seiten, Format (B × H): 156 mm x 234 mm, Gewicht: 1880 g

Reihe: NATO Science Series II: Mathematics, Physics and Chemistry

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.

Zielgruppe

Research

Autoren/Hrsg.

Wiersma, Dirk

Wall, C T C

Zakalyukin, V.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Topologie Analytische Topologie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

A: Singularities of real maps.- Classifications in Singularity Theory and Their Applications.- Applications of Flag Contact Singularities.- On Stokes Sets.- Resolutions of discriminants and topology of their complements.- Classifying Spaces of Singularities and Thorn Polynomials.- Singularities and Noncommutative Geometry.- B: Singular complex varietes.- The Geometry of Families of Singular Curves.- On the preparation theorem for subanalytic functions.- Computing Hodge-theoretic invariants of singularities.- Frobenius manifolds and variance of the spectral numbers.- Monodromy and Hodge Theory of Regular Functions.- Bifurcations and topology of meromorphic germs.- Unitary reflection groups and automorphisms of simple, hypersurface singularities.- Simple Singularities and Complex Reflections.- C: Singularities of holomorphic maps.- Discriminants, vector fields and singular hypersurfaces.- The theory of integral closure of ideals and modules: Applications and new developments.- Nonlinear Sections of Nonisolated Complete Intersections.- The Vanishing Topology of Non Isolated Singularities.