Jumping Numbers on Algebraic Surfaces with Rational Singularities
Algebraic Geometry
2008-02-17 v2
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 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.
Cite
@article{arxiv.0801.0734,
title = {Jumping Numbers on Algebraic Surfaces with Rational Singularities},
author = {Kevin Tucker},
journal= {arXiv preprint arXiv:0801.0734},
year = {2008}
}
Comments
Replaced Introduction, Includes Minor Revisions