**Contemporary Mathematics**

Volume: 459;
2008;
261 pp;
Softcover

MSC: Primary 32; 53; 34; 14;

Print ISBN: 978-0-8218-4497-7

Product Code: CONM/459

List Price: $86.00

AMS Member Price: $68.80

MAA Member Price: $77.40

**Electronic ISBN: 978-0-8218-8138-5
Product Code: CONM/459.E**

List Price: $86.00

AMS Member Price: $68.80

MAA Member Price: $77.40

# Real and Complex Singularities

Share this page *Edited by *
*Marcelo J. Saia; José Seade*

This book offers a selection of papers based on talks presented at the Ninth
International Workshop on Real and Complex Singularities, a series of biennial
workshops organized by the Singularity Theory group at São Carlos,
S.P., Brazil. The papers deal with all the different topics in
singularity theory and its applications, from pure singularity theory
related to commutative algebra and algebraic geometry to those topics
associated with various aspects of geometry to homotopy theory.

Among the topics on pure singularity theory discussed are invariants
of singularities, integral closure and equisingularity, classification
theory, contact structures and vector fields, and Thom polynomials.
Geometric aspects deal with relations of singularity theory with
topology, differential geometry and physics. Here topics discussed
include the index of quadratic differential forms, obstructions in
fundamental groups of plane curve complements, conjugate vectors of
immersed manifolds, exotic moduli of Goursat distributions in
codimension three, cobordisms of fold maps, etc. The book concludes
with notes from the course on the residue theoretical approach to
intersection theory.

#### Readership

Graduate students and research mathematicians interested in singularity theory and applications to dynamical systems, physics, and geometry.

# Table of Contents

## Real and Complex Singularities

- Contents v6 free
- Preface vii8 free
- Conjugate Vectors of Immersed Manifolds 110 free
- Invariants of D(q,p) Singularities 1322
- Nilpotents, Integral Closure and Equisingularity Conditions 2332
- Singularities in Generic One-parameter Complex Analytic Families of Maps 3544
- Global Classification of Curves on the Symplectic Plane 5160
- Counting Isolated Singularities of a Stable Perturbation of a Finitely A-determined Map-germ (Cn, 0) → ( CP, 0), with n < p 7382
- Milnor Numbers and Equisingularity of Map Germs from Cn+3 to C3 8796
- Cobordism Invariants of Fold Maps 103112
- Obstructions on Fundamental Groups of Plane Curve Complements 117126
- Exotic Moduli of Goursat Distributions Exist Already in Codimension Three 131140
- Hypersurfaces with Isolated Singularities with Symmetry 147156
- Thom Polynomials and Schur Functions: Towards theSingularities Ai(–) 165174
- Index of Quadratic Differential Forms 179188 free
- Remarks on Contact Structures and Vector Fields on Isolated Complete Intersection Singularities 195204
- Residue Theoretical Approach to Intersection Theory 207216
- 1. Chern classes via obstruction theory 209218
- 2. Čech-de Rham cohomology 213222
- 3. Chern-Weil theory adapted to the Čech-de Rham cohomology 218227
- 4. Residues of Chern classes on manifolds 226235
- 5. Localization on singular varieties 232241
- 6. Residues of Chern classes on singular varieties 237246
- 7. Intersections in complex manifolds 243252
- 7.1. Intersection product with a subvariety 244253
- 7.2. Poincaré and Alexander dualities revisited 244253
- 7.3. Intersections of analytic subspaces 246255
- 7.4. Subspaces defined by γ-sections 247256
- 7.5. Intersections of subspaces defined by regular sections 249258
- 7.6. Multiplicity at a point 250259

- 8. Intersections in singular varieties 251260
- 9. Intersection theory on singular surfaces and an application 254263
- References 258267