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Jumping numbers on algebraic surfaces with rational singularities

Author: Kevin Tucker
Journal: Trans. Amer. Math. Soc. 362 (2010), 3223-3241
MSC (2000): Primary 14B05
Published electronically: December 17, 2009
MathSciNet review: 2592954
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Abstract: In this article, we study the jumping numbers of an ideal in the local ring at rational singularity on a complex algebraic surface. By understanding the contributions of reduced divisors on a fixed resolution, we are able to present an algorithm for finding the jumping numbers of the ideal. This shows, in particular, how to compute the jumping numbers of a plane curve from the numerical data of its minimal resolution. In addition, the jumping numbers of the maximal ideal at the singular point in a Du Val or toric surface singularity are computed, and applications to the smooth case are explored.

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Additional Information

Kevin Tucker
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

Received by editor(s): April 9, 2008
Received by editor(s) in revised form: August 27, 2008
Published electronically: December 17, 2009
Additional Notes: The author was partially supported by the NSF under grant DMS-0502170.
Dedicated: In memory of Juha Heinonen
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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