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

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arxiv 1711.09530 v3 pith:FMP2MEWZ submitted 2017-11-27 math.DG math.AG

Chi Li , Gang Tian , Feng Wang This is my paper · ORCID
classification math.DGmath.AG
keywords fanovarietiesconjecturemathbbsingularsmoothvarietyyau-tian-donaldson
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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 K\"{a}hler-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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  1. Existence of Kahler-Ricci solitons on smoothable Q-Fano varities

    math.DG 2019-08 conditional novelty 6.0 of 10

    K-stable smoothable Q-Fano varieties admit Kähler-Ricci solitons, extending the Yau-Tian-Donaldson correspondence for solitons from the smooth case to the singular smoothable case.

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