K-stability of Fano spherical varieties

IF 1.3 1区数学 Q1 MATHEMATICS

Annales Scientifiques De L Ecole Normale Superieure Pub Date : 2016-08-05 DOI:10.24033/ASENS.2430

Thibaut Delcroix

引用次数: 57

Abstract

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.

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Fano球形品种的k -稳定性

利用Q-Fano球变体的矩多面体和一些与开放轨道相关的组合数据，证明了Q-Fano球变体关于等变特殊试验构形的k稳定性的一个组合判据。结合Datar和Szekelyhidi证明的关于Fano流形的you - tian - donaldson猜想的等变版本，给出了球面Fano流形上Kahler-Einstein度规存在的判据。结果也适用于修正k稳定性和Kahler-Ricci孤子的存在性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales Scientifiques De L Ecole Normale Superieure 数学-数学

CiteScore

3.00

自引率

5.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Annales scientifiques de l''École normale supérieure were founded in 1864 by Louis Pasteur. The journal dealt with subjects touching on Physics, Chemistry and Natural Sciences. Around the turn of the century, it was decided that the journal should be devoted to Mathematics. Today, the Annales are open to all fields of mathematics. The Editorial Board, with the help of referees, selects articles which are mathematically very substantial. The Journal insists on maintaining a tradition of clarity and rigour in the exposition. The Annales scientifiques de l''École normale supérieures have been published by Gauthier-Villars unto 1997, then by Elsevier from 1999 to 2007. Since January 2008, they are published by the Société Mathématique de France.