K-stability of Fano spherical varieties

By Thibaut Delcroix. 2016

71 citations recorded by the source corpus.

We prove a combinatorial criterion for K-stability of a Q-Fano spherical variety with respect to equivariant special test configurations, in terms of its moment polytope and some combinatorial data associated to the open orbit. Combined with the equivariant version of the Yau-Tian-Donaldson conjecture for Fano manifolds proved by Datar and Szekelyhidi, it yields a criterion for the existence of a Kahler-Einstein metric on a spherical Fano manifold. The results hold also for modified K-stability and existence of Kahler-Ricci solitons.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/c76a8dbdbd5fdf3580372a5d7ddd915c8283a010

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In Applied Mathematics

1. Chenyang Xu
2. Jiyuan Han
3. Chi Li
4. Yuchen Liu
5. H. Blum
6. Ziquan Zhuang
7. Mattias Jonsson
8. Xiaowei Wang

In Geometry and Topology

1. Chenyang Xu
2. Jiyuan Han
3. Chi Li
4. Yuchen Liu
5. H. Blum
6. Ziquan Zhuang
7. Mattias Jonsson
8. Xiaowei Wang

Citations in the corpus

• K-stability of Fano varieties: an algebro-geometric approach (2020, methodology): “reductive group G) acts on X implies K-semistability (resp. K-polystability). This provides a powerful tool to verify K-(semi,poly)stability of a Fano variety X when it has a large symmetry (see e.g. [Del20]). 10. ExplicitK-moduli spaces We can also prove a Q-Fano variety is K-(semi,poly)-stable by ”
• On the Yau‐Tian‐Donaldson Conjecture for Generalized Kähler‐Ricci Soliton Equations (2020, methodology): “More generally, similar applications can be applied to -varieties of complexity one (see [21, 47]) and spherical varieties as in [29] or Fano -varieties (for a reductive complex Lie group ) as in [63].”