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On minimal log discrepancies and kollár components

Part of: Local theory Birational geometry

Published online by Cambridge University Press:  04 November 2021

Joaquín Moraga
Joaquín Moraga*
Affiliation:
Department of Mathematics, University of Utah, 155 S 1400 E, JWB 321, Salt Lake City, UT 84112, USA ([email protected])
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Abstract

In this article, we prove a local implication of boundedness of Fano varieties. More precisely, we prove that $d$-dimensional $a$-log canonical singularities with standard coefficients, which admit an $\epsilon$-plt blow-up, have minimal log discrepancies belonging to a finite set which only depends on $d,\,a$ and $\epsilon$. This result gives a natural geometric stratification of the possible mld's in a fixed dimension by finite sets. As an application, we prove the ascending chain condition for minimal log discrepancies of exceptional singularities. We also introduce an invariant for klt singularities related to the total discrepancy of Kollár components.

Keywords

log terminalKollar componentslog discrepancies

MSC classification

Primary: 14E30: Minimal model program (Mori theory, extremal rays)
Secondary: 14B05: Singularities
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 64 , Issue 4 , November 2021 , pp. 982 - 1001
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Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press on Behalf of The Edinburgh Mathematical Society

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