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arXiv · 1711.09530

On the Yau-Tian-Donaldson conjecture for singular Fano varieties

Chi Li·Gang Tian·Feng Wang
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Abstract

We prove the Yau-Tian-Donaldson's conjecture for any $\mathbb{Q}$-Fano variety that has a log smooth resolution of singularities such that the discrepancies of all exceptional divisors are non-positive. 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 $\mathbb{Q}$-Fano varieties, which include those admitting crepant log resolutions.

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BibTeXRIS

Chi Li, Gang Tian, Feng Wang. 2021-03-29. On the Yau-Tian-Donaldson conjecture for singular Fano varieties. https://arxiv.org/abs/1711.09530

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