English

Shokurov's ACC Conjecture for log canonical thresholds on smooth varieties

Algebraic Geometry 2019-12-19 v3

Abstract

Shokurov conjectured that the set of all log canonical thresholds on varieties of bounded dimension satisfies the ascending chain condition. In this paper we prove that the conjecture holds for log canonical thresholds on smooth varieties and, more generally, on locally complete intersection varieties and on varieties with quotient singularities.

Keywords

Cite

@article{arxiv.0905.3775,
  title  = {Shokurov's ACC Conjecture for log canonical thresholds on smooth varieties},
  author = {Tommaso de Fernex and Lawrence Ein and Mircea Mustata},
  journal= {arXiv preprint arXiv:0905.3775},
  year   = {2019}
}

Comments

20 pages. This supersedes arXiv:0811.4642 and arXiv:0811.4644. As opposed to these older versions, we now give a proof of Koll\'ar's m-adic semicontinuity result using only the Connectedness Theorem; v.3: section 4 has been rewritten; to appear in Duke Math. J