题目: Yau-Tian-Donaldson conjecture for generalized Kähler-Ricci soliton equations

报告人：Jiyuan Han(Purdue University) 

时间: 2020年11月13日, 周五，上午7：50-9：20  

地点：腾讯会议账号:950 391 9321 ; 密码112358

摘要：Let (X,D) be a log variety with an effective holomorphic torus action, and Θ be a closed positive (1,1)-current. For any smooth positive function g defined on the moment polytope of the torus action, we study the Monge-Ampere equations that correspond to generalized and twisted Kahler-Ricci g-solitons. We prove a version of Yau-Tian-Donaldson (YTD) conjecture for these general equations, showing that the existence of solutions is always equivalent to an equivariantly uniform Θ-twisted g-Ding-stability. When Θ is a current associated to a torus invariant linear system, we further show that equivariant special test configurations suffice for testing the stability. Our results allow arbitrary klt singularities and generalize most of previous results on (uniform) YTD conjecture for (twisted) Kahler-Ricci/Mabuchi solitons or Kahler-Einstein metrics. This is a joint work with Chi Li.

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