Title:

On K-polystability of Csck Manifolds with Transcendental  Cohomology Class

Time:

10:10 am - 12:00 pm, March 16, Friday 

Venue: 

Room 82J04, Jiayibing Building, Jingchunyuan 82, BICMR

Speaker: 

Dr. Zakarias Sjöström Dyrefelt (Chalmers University of Technology)

Abstract:
Over the course of two talks we will discuss possible generalizations of Tian's K-polystability notion to compact Kähler 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 Kähler (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.