ON THE K-STABILITY OF FANO VARIETIES AND ANTICANONICAL DIVISORS

被引：71

作者：

Fujita, Kento ^{[1
]}

Odaka, Yuji ^{[2
]}

机构：

[1] Kyoto Univ, Res Inst Math Sci, Kyoto 6068502, Japan

[2] Kyoto Univ, Dept Math, Kyoto 6068502, Japan

来源：

TOHOKU MATHEMATICAL JOURNAL | 2018年 / 70卷 / 04期

关键词：

Fano varieties; K-stability; Kahler-Einstein metrics; KAHLER-EINSTEIN METRICS; COMPACT MODULI SPACES; SCALAR CURVATURE; MANIFOLDS; LIMITS; BOUNDS;

D O I：

10.2748/tmj/1546570823

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We apply a recent theorem of Li and the first author to give some criteria for the K-stability of Fano varieties in terms of anticanonical Q-divisors. First, we propose a condition in terms of certain anti-canonical Q-divisors of given Fano variety, which we conjecture to be equivalent to the K-stability. We prove that it is at least a sufficient condition and also related to the Berman-Gibbs stability. We also give another algebraic proof of the K-stability of Fano varieties which satisfy Tian's alpha invariants condition.

引用

页码：511 / 521

页数：11

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