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Jumping numbers of a simple complete ideal in a two-dimensional regular local ring
About this Title
Tarmo Järvilehto, Pääskykuja 5, 04620 Mäntsälä, Finland
Publication: Memoirs of the American Mathematical Society
Publication Year:
2011; Volume 214, Number 1009
ISBNs: 978-0-8218-4811-1 (print); 978-1-4704-0626-4 (online)
DOI: https://doi.org/10.1090/S0065-9266-2011-00597-6
Published electronically: April 4, 2011
Keywords: Multiplier ideals,
log-canonical threshold,
plane curve singularity
MSC: Primary 13H05; Secondary 14B05
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
Abstract
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 we shall give an explicit formula for the jumping numbers of a simple complete ideal in a two-dimensional regular local ring. In particular, we obtain a formula for the jumping numbers of an analytically irreducible plane curve. We then show that the jumping numbers determine the equisingularity class of the curve.
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