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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Jumping numbers on algebraic surfaces with rational singularities
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by Kevin Tucker PDF
Trans. Amer. Math. Soc. 362 (2010), 3223-3241 Request permission

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
  • Email: kevtuck@umich.edu
  • 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
  • © Copyright 2009 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 3223-3241
  • MSC (2000): Primary 14B05
  • DOI: https://doi.org/10.1090/S0002-9947-09-04956-3
  • MathSciNet review: 2592954