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JUMPING NUMBERS ON ALGEBRAIC SURFACES WITH RATIONAL SINGULARITIES

KEVIN TUCKER
Transactions of the American Mathematical Society
Vol. 362, No. 6 (JUNE 2010), pp. 3223-3241
Stable URL: http://www.jstor.org/stable/25677824
Page Count: 19
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
JUMPING NUMBERS ON ALGEBRAIC SURFACES WITH RATIONAL SINGULARITIES
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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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