**Contemporary Mathematics**

Volume: 266;
2000;
187 pp;
Softcover

MSC: Primary 13; 14; 32;

Print ISBN: 978-0-8218-2005-6

Product Code: CONM/266

List Price: $60.00

Individual Member Price: $48.00

**Electronic ISBN: 978-0-8218-7856-9
Product Code: CONM/266.E**

List Price: $60.00

Individual Member Price: $48.00

# Singularities in Algebraic and Analytic Geometry

Share this page *Edited by *
*Caroline Grant Melles; Ruth I. Michler*

This volume contains the proceedings of an AMS special session held at the 1999 Joint Mathematics Meetings in San Antonio. The participants were an international group of researchers studying singularities from algebraic and analytic viewpoints. The contributed papers contain original results as well as some expository and historical material. This volume is dedicated to Oscar Zariski, on the one hundredth anniversary of his birth.

Topics include the role of valuation theory in algebraic geometry with recent applications to the structure of morphisms; algorithmic approaches to resolution of equisingular surface singularities and locally toric varieties; weak subintegral closures of ideals and Rees valuations; constructions of universal weakly subintegral extensions of rings; direct-sum decompositions of finitely generated modules; construction and examples of resolution graphs of surface singularities; Jacobians of meromorphic curves; investigation of spectral numbers of curve singularities using Puiseux pairs; Gröbner basis calculations of Hochschild homology for hypersurfaces with isolated singularities; and the theory of characteristic classes of singular spaces—a brief history with conjectures and open problems.

#### Table of Contents

# Table of Contents

## Singularities in Algebraic and Analytic Geometry

- Contents vii8 free
- Preface ix10 free
- AMS special session on singularities in algebraic and analytic geometry xi12 free
- Factoring the Jacobian 114 free
- Weak normalization and weak subintegral closure 1124
- Integral dependence and weak subintegrality 2336
- Singularities and direct-sum decompositions 2942
- Valuations in algebra and geometry 4558
- Simultaneous resolution of equisingular quasi-ordinary singularities 6578
- Single-step combinatorial resolution via coherent sheaves of ideals 7790
- Resolution graphs of some surface singularities, I. (Cyclic coverings) 89102
- Resolution graphs of some surface singularities, II. (Generalized Iomdin series) 129142
- Inequalities for spectral distributions of curve singularities 165178
- Isolated singularities with large Hochschild homology 171184
- Milnor classes via polar varieties 181194

#### Readership

Graduate students and research mathematicians interested in singularities, algebraic geometry, analytic geometry or commutative algebra with an interest in singularities.