eBook ISBN: | 978-1-4704-0626-4 |
Product Code: | MEMO/214/1009.E |
List Price: | $70.00 |
MAA Member Price: | $63.00 |
AMS Member Price: | $42.00 |
eBook ISBN: | 978-1-4704-0626-4 |
Product Code: | MEMO/214/1009.E |
List Price: | $70.00 |
MAA Member Price: | $63.00 |
AMS Member Price: | $42.00 |
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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 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.
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Table of Contents
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Chapters
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1. Introduction
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2. Preliminaries on Complete Ideals
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3. Arithmetic of the Point Basis
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4. The Dual Graph
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5. Multiplier Ideals and Jumping Numbers
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6. Main Theorem
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7. Proof of Main Theorem
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8. Jumping Numbers of a Simple Ideal
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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 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.
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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