Jumping Numbers on Algebraic Surfaces with Rational Singularities

Details Jumping Numbers on Algebraic Surfaces with Rational Singularities Jumping Numbers on Algebraic Surfaces with Rational Singularities

2008-01-04

arxiv.org/abs/0801.0734v2

Mathematics

Algebraic Geometry

Replaced Introduction, Includes Minor Revisions

Scientific paper

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 of 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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