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On minimal log discrepancies and kollár components
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 64 / Issue 4 / November 2021
- Published online by Cambridge University Press:
- 04 November 2021, pp. 982-1001
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- Article
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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.
