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Bull. Korean Math. Soc. 2021; 58(1): 113-132

Online first article December 28, 2020      Printed January 31, 2021

https://doi.org/10.4134/BKMS.b200052

Copyright © The Korean Mathematical Society.

On divisors computing mld's and lct's

Harold Blum

University of Utah

Abstract

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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 prove a result describing which divisors compute asymptotic log canonical thresholds.

Keywords: Singularities, log canonical thresholds, graded sequences of ideals

MSC numbers: 14B05

Supported by: This work was partially supported by NSF grant DMS-0943832

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