Jumping Numbers of a Simple Complete Ideal in a Two-Dimensional Regular Local Ring

Released on by Tarmo Järvilehto
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  • Jumping Numbers of a Simple Complete Ideal in a Two-Dimensional Regular Local Ring Book Detail

  • Author : Tarmo Järvilehto
  • Release Date : 2011
  • Publisher : American Mathematical Soc.
  • Genre : Mathematics
  • Pages : 93
  • ISBN 13 : 0821848119
  • File Size : 55,55 MB
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Jumping Numbers of a Simple Complete Ideal in a Two-Dimensional Regular Local Ring by Tarmo Järvilehto PDF Summary

Book Description: 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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