Classification of Algebraic Varieties
Full-Text PDF (533 KB) | Book articles | Book details
(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.