# 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.

#### Readership

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

# 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