GEODESIC RAYS AND KAHLER-RICCI TRAJECTORIES ON FANO MANIFOLDS

被引：14

作者：

Darvas, Tamas ^{[1
]}

He, Weiyong ^{[2
]}

机构：

[1] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[2] Univ Oregon, Dept Math, Eugene, OR 97403 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2017年 / 369卷 / 07期

基金：

美国国家科学基金会;

关键词：

MULTIPLIER IDEAL SHEAVES; EINSTEIN METRICS; MONGE-AMPERE; TEST CONFIGURATIONS; FLOW; SPACE; ENERGY; POTENTIALS; REGULARITY; VARIETIES;

D O I：

10.1090/tran/6878

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose (X, J, omega) is a Fano manifold and t -> gamma(t) is a diverging Kahler-Ricci trajectory. We construct a bounded geodesic ray t -> u(t) weakly asymptotic to t -> gamma(t), along which Ding's.F functional decreases, partially confirming a folklore conjecture. In the absence of non-trivial holomorphic vector fields this proves the equivalence between geodesic stability of the functional and existence of Kahler-Einstein metrics. We also explore applications of our construction to Tian's alpha-invariant.

引用

页码：5069 / 5085

页数：17