On the Yau-Tian-Donaldson Conjecture for Singular Fano Varieties

Chi Li, Gang Tian, Feng Wang

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We prove the Yau-Tian-Donaldson conjecture for any ℚ-Fano variety that has a log smooth resolution of singularities such that a negative linear combination of exceptional divisors is relatively ample and the discrepancies of all exceptional divisors are nonpositive. In other words, if such a Fano variety is K-polystable, then it admits a Kähler-Einstein metric. This extends the previous result for smooth Fano varieties to this class of singular ℚ-Fano varieties, which includes all ℚ-factorial ℚ-Fano varieties that admit crepant log resolutions.

Original languageEnglish (US)
Pages (from-to)1748-1800
Number of pages53
JournalCommunications on Pure and Applied Mathematics
Issue number8
StatePublished - Aug 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics


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