Jumping numbers and ordered tree structures on the dual graph

Details Jumping numbers and ordered tree structures on the dual graph Jumping numbers and ordered tree structures on the dual graph

2010-01-08

arxiv.org/abs/1001.1220v2

Mathematics

Commutative Algebra

26 pages, a reference added, some typos corrected, to appear in Manuscripta Mathematica

Scientific paper

Let R be a two-dimensional regular local ring having an algebraically closed residue field and let a be a complete ideal of finite colength in R. In this article we investigate the jumping numbers of a by means of the dual graph of the minimal log resolution of the pair (X,a). Our main result is a combinatorial criterium for a positive rational number to be a jumping number. In particular, we associate to each jumping number certain ordered tree structures on the dual graph.

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