Jumping Number Contribution on Algebraic Surfaces with an Isolated Rational Singularity
نویسندگان
چکیده
Given an ideal in the local ring at a rational surface singularity, we define what it means for a collection of exceptional divisors on a fixed log resolution to critically contribute a jumping number. This is shown to be a numerical property of the collection, and can be used to give an explicit algorithm for finding all of the jumping numbers of the ideal. In addition, the jumping numbers of the maximal ideal at the singular point in an isolated Du Val or toric surface singularity are computed, and applications to the smooth case are explored.
منابع مشابه
Jumping Numbers on Algebraic Surfaces with Rational Singularities
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...
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