On minimal log discrepancies and kollár components

Research output: Contribution to journalArticlepeer-review

Abstract

In this article, we prove a local implication of boundedness of Fano varieties. More precisely, we prove that-dimensional-log canonical singularities with standard coefficients, which admit an-plt blow-up, have minimal log discrepancies belonging to a finite set which only depends on and. 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.

Original languageEnglish (US)
Pages (from-to)982-1001
Number of pages20
JournalProceedings of the Edinburgh Mathematical Society
Volume64
Issue number4
DOIs
StatePublished - Nov 4 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

  • Kollar components
  • Log discrepancies
  • Log terminal

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