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Jumping Numbers of a Simple Complete Ideal in a Two-Dimensional Regular Local Ring
 
Jumping Numbers of a Simple Complete Ideal in a Two-Dimensional Regular Local Ring
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
Jumping Numbers of a Simple Complete Ideal in a Two-Dimensional Regular Local Ring
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Jumping Numbers of a Simple Complete Ideal in a Two-Dimensional Regular Local Ring
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
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2142011; 78 pp
    MSC: 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.

  • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2142011; 78 pp
MSC: 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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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