**Memoirs of the American Mathematical Society**

2011;
78 pp;
Softcover

MSC: Primary 13;
Secondary 14

Print ISBN: 978-0-8218-4811-1

Product Code: MEMO/214/1009

List Price: $70.00

AMS Member Price: $42.00

MAA Member Price: $63.00

**Electronic ISBN: 978-1-4704-0626-4
Product Code: MEMO/214/1009.E**

List Price: $70.00

AMS Member Price: $42.00

MAA Member Price: $63.00

# Jumping Numbers of a Simple Complete Ideal in a Two-Dimensional Regular Local Ring

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*Tarmo Järvilehto*

The multiplier ideals of an ideal in a regular local ring
form a family of ideals parameterized by non-negative rational
numbers. As the rational number increases the corresponding multiplier
ideal remains unchanged until at some point it gets strictly
smaller. A rational number where this kind of diminishing occurs is
called a jumping number of the ideal.

In this manuscript the
author gives an explicit formula for the jumping numbers of a simple
complete ideal in a two-dimensional regular local ring. In particular,
he obtains a formula for the jumping numbers of an analytically
irreducible plane curve. He then shows that the jumping numbers
determine the equisingularity class of the curve.

#### Table of Contents

# Table of Contents

## Jumping Numbers of a Simple Complete Ideal in a Two-Dimensional Regular Local Ring

- List of Figures vii8 free
- Chapter 1. Introduction 110 free
- Chapter 2. Preliminaries on Complete Ideals 514 free
- Chapter 3. Arithmetic of the Point Basis 1322
- Chapter 4. The Dual Graph 1928
- Chapter 5. Multiplier Ideals and Jumping Numbers 2534
- Chapter 6. Main Theorem 2938
- Chapter 7. Proof of Main Theorem 3544
- Chapter 8. Jumping Numbers of a Simple Ideal 5968
- Chapter 9. Jumping Numbers of an Analytically Irreducible Plane Curve 6978
- Bibliography 7786