English

Jumping numbers and ordered tree structures on the dual graph

Commutative Algebra 2011-03-24 v2 Algebraic Geometry

Abstract

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.

Keywords

Cite

@article{arxiv.1001.1220,
  title  = {Jumping numbers and ordered tree structures on the dual graph},
  author = {Eero Hyry and Tarmo Järvilehto},
  journal= {arXiv preprint arXiv:1001.1220},
  year   = {2011}
}

Comments

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

R2 v1 2026-06-21T14:32:15.868Z