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.
All Science Journal Classification (ASJC) codes
- Applied Mathematics