Uniqueness of K-polystable degenerations of Fanovarieties

Harold Blum, Chenyang Xu

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


We prove that K-polystable degenerations of ℚ -Fano varieties are unique. Furthermore, we show that the moduli stack of K-stable ℚ-Fano varieties is separated. Together with recently proven boundedness and openness statements, the latter result yields a separated Deligne-Mumford stack parametrizing all uniformly K-stable ℚ-Fano varieties of fixed dimension and volume. The result also implies that the automorphism group of a K-stable ℚ-Fano variety is finite.

Original languageEnglish (US)
Pages (from-to)609-656
Number of pages48
JournalAnnals of Mathematics
Issue number2
StatePublished - 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Degenerations
  • Fano varieties
  • K-stability
  • Moduli


Dive into the research topics of 'Uniqueness of K-polystable degenerations of Fanovarieties'. Together they form a unique fingerprint.

Cite this