On K-polystability of Csck Manifolds with Transcendental Cohomology Class (Ⅱ)
Time: 2018-03-19
Published By: Ningbo Lu
Speaker(s): Zakarias Sjöström Dyrefelt (Chalmers University of Technology)
Time: 09:00-11:00 March 20, 2018
Venue: 请选择
Title:
On K-polystability of Csck Manifolds with Transcendental Cohomology Class
Time:
09:00 am - 11:00 am, March 20, Tuesday
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.
On K-polystability of Csck Manifolds with Transcendental Cohomology Class
Time:
09:00 am - 11:00 am, March 20, Tuesday
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.
