English

Log canonical thresholds on varieties with bounded singularities

Algebraic Geometry 2010-06-25 v2

Abstract

We consider pairs (X,A), where X is a variety with klt singularities and A is a formal product of ideals on X with exponents in a fixed set that satisfies the Descending Chain Condition. We also assume that X has (formally) bounded singularities, in the sense that it is, formally locally, a subvariety in a fixed affine space defined by equations of bounded degree. We prove in this context a conjecture of Shokurov, predicting that the set of log canonical thresholds for such pairs satisfies the Ascending Chain Condition.

Keywords

Cite

@article{arxiv.1004.3336,
  title  = {Log canonical thresholds on varieties with bounded singularities},
  author = {Tommaso de Fernex and Lawrence Ein and Mircea Mustata},
  journal= {arXiv preprint arXiv:1004.3336},
  year   = {2010}
}

Comments

38 pages; v.2: minor changes, to appear in the proceedings of the conference `Classification of algebraic varieties' at Schiermonnikoog

R2 v1 2026-06-21T15:12:22.311Z