4.6 Article

A VARIATIONAL APPROACH TO THE YAU-TIAN-DONALDSON CONJECTURE

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On theYau-Tian-DonaldsonConjecture for Singular Fano Varieties

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Summary: In this study, it was proven that a double-struck capital Q-Fano variety with a log smooth resolution of singularities, where a negative linear combination of exceptional divisors is relatively ample and the discrepancies of exceptional divisors are nonpositive, is K-polystable and admits a Kahler-Einstein metric. This extends previous results on smooth Fano varieties to this class of singular double-struck capital Q-Fano varieties, including those that admit crepant log resolutions.

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