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Jumping Numbers of a Simple Complete Ideal in a Two-Dimensional Regular Local Ring
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Memoirs of the American Mathematical Society
2011; 78 pp; softcover
Volume: 214
ISBN-10: 0-8218-4811-9
ISBN-13: 978-0-8218-4811-1
List Price: US$66 Individual Members: US$39.60
Institutional Members: US\$52.80
Order Code: MEMO/214/1009

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.

• Introduction
• Preliminaries on complete ideals
• Arithmetic of the point basis
• The dual graph
• Multiplier ideals and jumping numbers
• Main theorem
• Proof of main theorem
• Jumping numbers of a simple ideal
• Jumping numbers of an analytically irreducible plane curve
• Bibliography