On the <scp>Yau‐Tian‐Donaldson</scp> Conjecture for Singular Fano Varieties

Abstract

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. © 2020 Wiley Periodicals LLC