On divisors computing MLD's and LCT's

Abstract

We show that if a divisor centered over a point on a smooth surface computes a minimal log discrepancy, then the divisor also computes a log canonical threshold. To prove the result, we study the asymptotic log canonical threshold of the graded sequence of ideals associated to a divisor over a variety. We systematically study this invariant and also prove a result describing which divisors compute asymptotic log canonical thresholds.

Minor corrections and changes. Comments welcome

References in corpus (2)

• Finiteness of algebraic fundamental groups
• Divisors computing the minimal log discrepancy on a smooth surface

Cited by in corpus (5)

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• Uniqueness of K-polystable degenerations of Fano varieties
• Igusa's conjecture for exponential sums: optimal estimates for non-rational singularities
• Divisors computing the minimal log discrepancy on a smooth surface
• Higher Codimensional Alpha Invariants and Characterization of Projective Spaces