eBook ISBN:  9781470406264 
Product Code:  MEMO/214/1009.E 
List Price:  $70.00 
MAA Member Price:  $63.00 
AMS Member Price:  $42.00 
eBook ISBN:  9781470406264 
Product Code:  MEMO/214/1009.E 
List Price:  $70.00 
MAA Member Price:  $63.00 
AMS Member Price:  $42.00 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 214; 2011; 78 ppMSC: Primary 13; Secondary 14;
The multiplier ideals of an ideal in a regular local ring form a family of ideals parameterized by nonnegative 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 twodimensional 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

Chapters

1. Introduction

2. Preliminaries on Complete Ideals

3. Arithmetic of the Point Basis

4. The Dual Graph

5. Multiplier Ideals and Jumping Numbers

6. Main Theorem

7. Proof of Main Theorem

8. Jumping Numbers of a Simple Ideal

9. Jumping Numbers of an Analytically Irreducible Plane Curve


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The multiplier ideals of an ideal in a regular local ring form a family of ideals parameterized by nonnegative 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 twodimensional 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.

Chapters

1. Introduction

2. Preliminaries on Complete Ideals

3. Arithmetic of the Point Basis

4. The Dual Graph

5. Multiplier Ideals and Jumping Numbers

6. Main Theorem

7. Proof of Main Theorem

8. Jumping Numbers of a Simple Ideal

9. Jumping Numbers of an Analytically Irreducible Plane Curve