Jumping numbers on algebraic surfaces with rational singularities

Tucker, Kevin

doi:10.1090/S0002-9947-09-04956-3

Jumping numbers on algebraic surfaces with rational singularities
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by Kevin Tucker

Trans. Amer. Math. Soc. 362 (2010), 3223-3241

DOI: https://doi.org/10.1090/S0002-9947-09-04956-3

Published electronically: December 17, 2009

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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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