Stability of valuations and Kollár components

Chi Li, Chenyang Xu

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


We prove that among all Kollár components obtained by plt blow ups of a klt singularity o ∈ (X, D), there is at most one that is (log-)K-semistable. We achieve this by showing that if such a Kollár component exists, it uniquely minimizes the normalized volume function introduced in [Li18] among all divisorial valuations. Conversely, we show that any divisorial minimizer of the normalized volume function yields a K-semistable Kollár component. We also prove that for any klt singularity, the infimum of the normalized volume function is always approximated by the normalized volumes of Kollár components.

Original languageEnglish (US)
Pages (from-to)2573-2627
Number of pages55
JournalJournal of the European Mathematical Society
Issue number8
StatePublished - 2020
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


  • K-stability
  • Klt singularity
  • Kollár component
  • Normalized volume


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