On K-polystability of Csck Manifolds with Transcendental Cohomology Class (Ⅱ)
主 题: On K-polystability of Csck Manifolds with Transcendental Cohomology Class (Ⅱ)
报告人: Zakarias Sj?str?m Dyrefelt (Chalmers University of Technology)
时 间: 2018-03-20 09:00 - 2018-03-20 11:00
地 点: 请选择
Title:<\/strong>
\nOn K-polystability of Csck Manifolds with Transcendental Cohomology Class<\/strong>
\nTime:<\/strong>
\n09:00 am - 11:00 am, March 20, Tuesday
\nVenue: <\/strong>
\nRoom 82J04, Jiayibing Building, Jingchunyuan 82, BICMR
\nSpeaker:
\nDr. Zakarias Sj?str?m Dyrefelt (Chalmers University of Technology)
\n
\nAbstract:
\nOver the course of two talks we will discuss possible generalizations of Tian\'s K-polystability notion to compact K?hler manifolds which are not necessarily projective, and allowed to admit holomorphic vector fields. In a first part we define K-polystability on the level of (1,1)-cohomology classes, and set up the necessary tools for exploiting the relationship between transcendental test configurations and subgeodesic rays. As a main result we then prove that constant scalar curvature K?hler (cscK) manifolds are geodesically K-polystable; a new notion which means that the Donaldson-Futaki invariant is always non-negative, and vanishes precisely if the test configuration is induced by a holomorphic vector field. As a corollary we prove one direction of various Yau-Tian-Donaldson conjectures in this setting.
