On equivalent conjectures for minimal log discrepancies on smooth threefolds

Kawakita, Masayuki

doi:10.1090/jag/757

Author: Masayuki Kawakita
Journal: J. Algebraic Geom. 30 (2021), 97-149
DOI: https://doi.org/10.1090/jag/757
Published electronically: June 2, 2020
MathSciNet review: 4233179
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Abstract | References | Additional Information

Abstract: On smooth varieties, the ACC for minimal log discrepancies is equivalent to the boundedness of the log discrepancy of some divisor which computes the minimal log discrepancy. In dimension three, we reduce it to the case when the boundary is the product of a canonical part and the maximal ideal to some power. We prove the reduced assertion when the log canonical threshold of the maximal ideal is either at most one-half or at least one.

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Additional Information

Masayuki Kawakita
Affiliation: Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan
MR Author ID: 680001
Email: masayuki@kurims.kyoto-u.ac.jp

Received by editor(s): May 16, 2018
Published electronically: June 2, 2020
Additional Notes: The author was partially supported by JSPS Grant-in-Aid for Scientific Research (C) 16K05099.
Article copyright: © Copyright 2020 University Press, Inc.