Symmetries, quotients and Kähler-Einstein metrics

By C. Arezzo, A. Ghigi, G. Pirola. 2004

50 citations recorded by the source corpus.

Abstract We consider Fano manifolds M that admit a collection of finite automorphism groups G 1, …, Gk , such that the quotients M/Gi are smooth Fano manifolds possessing a Kähler-Einstein metric. Under some numerical and smoothness assumptions on the ramification divisors, we prove that M admits a Kähler-Einstein metric too.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/33a4ec00047a958abab562a822ed7685f5becf13

How researchers see this paper

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In Applied Mathematics

1. G. Codogni
2. Ziquan Zhuang
3. Zsolt Patakfalvi

In Geometry and Topology

1. Ziquan Zhuang
2. G. Codogni
3. Zsolt Patakfalvi
4. Chenyang Xu

Citations in the corpus

• K-stability of Fano varieties via admissible flags (2020, unknown): “However, both criteria apply exclusively to certain Fano varieties of index one, and except in a few sporadic cases, it is unclear how to attack the problem when the required conditions in neither criterion are satisfied; see for example [1, 16, 38, 43].”
• Optimal destabilizing centers and equivariant K-stability (2020, methodology): “(2) [2] Complete intersection of two quadrics Q1 ∩ Q2 ⊆ Pn+2.”
• Positivity of the CM line bundle for families of K-stable klt Fano varieties (2020, background): “For the precise definition of the functor of MK-ss n,v we refer to [5,23].”