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

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.

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

References in corpus (4)

• Inversion of adjunction on log canonicity
• Desingularization of quasi-excellent schemes in characteristic zero
• Which powers of holomorphic functions are integrable?
• Invariants of singularities of pairs

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• IMPANGA lecture notes on log canonical thresholds
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• Ascending chain condition for $F$-pure thresholds on a fixed strongly $F$-regular germ
• A Minimizing Valuation is Quasi-monomial
• Existence of log canonical flips and a special LMMP
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• Discreteness of log discrepancies over log canonical triples on a fixed pair
• Ideal-adic semi-continuity of minimal log discrepancies on surfaces
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• A connectedness theorem over the spectrum of a formal power series ring
• Smooth 3-dimensional canonical thresholds
• Ascending chain condition for $F$-pure thresholds with fixed embedding dimension
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• Semi-continuity of Complex Singularity Exponents in Singular Central Fiber Cases
• On accumulation points of $F$-pure thresholds on regular local rings
• Uniform rationality of Poincaré series of p-adic equivalence relations and Igusa's conjecture on exponential sums
• Sequences of LCT-polytopes