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ISSN 1088-6850(e) ISSN 0002-9947(p)

Jumping numbers on algebraic surfaces with rational singularities

Author(s): Kevin Tucker
Journal: Trans. Amer. Math. Soc. 362 (2010), 3223-3241.
MSC (2000): Primary 14B05
Posted: December 17, 2009
MathSciNet review: 2592954
Retrieve article in: PDF

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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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