On the Yau‐Tian‐Donaldson Conjecture for Singular Fano Varieties

By Chi Li, G. Tian, Feng Wang. Communications on Pure and Applied Mathematics, 2017

47 citations recorded by the source corpus.

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

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/efcdf07bcdfdc9c5153fd2b9d7ec2570cf263b2c

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In Applied Mathematics

1. Chi Li
2. Feng Wang
3. G. Tian
4. Robert J. Berman
5. Yuchen Liu
6. Mattias Jonsson
7. Song Sun
8. Xiaowei Wang

In Geometry and Topology

1. Chi Li
2. Feng Wang
3. G. Tian
4. Robert J. Berman
5. Yuchen Liu
6. Mattias Jonsson
7. H. Blum
8. Song Sun

Citations in the corpus

• The Uniform Version of Yau–Tian–Donaldson Conjecture for Singular Fano Varieties (2019, methodology): “ natural to study such degenerate Monge-Am`ere equation using an appropriate sequence of non-degenerate Monge-Amp`ere equations to approximate the original equation, which is the guiding principle in [37]. The perturbative approach used here is motivated by this idea but is more on the non-Archimede”