Classification of Algebraic Varieties

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pp: 221–257

DOI: 10.4171/007-1/10

Log canonical thresholds on varieties with bounded singularities

Tommaso de Fernex[1], Lawrence Ein[2] and Mircea Mustaţă[3]

(1) University of Utah, Salt Lake City, USA
(2) University of Illinois at Chicago, USA
(3) University of Michigan, Ann Arbor, United States

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: Log canonical threshold, ascending chain condition.