主 题: On K-polystability of Csck Manifolds with Transcendental Cohomology Class
报告人: Zakarias Sj?str?m Dyrefelt (Chalmers University of Technology)
时 间: 2018-03-16 10:00 - 2018-03-20 17:00
地 点: Room 82J04, Jiayibing Building, Jingchunyuan 82, BICMR
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\n\t\tTitle:<\/strong><\/strong>\n\t<\/p>\n\t
\n\t\tOn K-polystability of Csck Manifolds with Transcendental Cohomology Class\n\t<\/p>\n<\/strong>\n<\/p>\n
\n\tTime:<\/strong>\n<\/p>\n
\n\t10:10 am - 12:00 pm, March 16, Friday \n<\/p>\n
\n\t15:00 pm - 17:00 pm, March 20, Tuesday\n<\/p>\n
\n\tVenue: <\/strong>\n<\/p>\n
\n\tRoom 82J04, Jiayibing Building, Jingchunyuan 82, BICMR\n<\/p>\n
\n\tSpeaker: <\/strong>\n<\/p>\n
\n\tProfessor Zakarias Sj?str?m Dyrefelt (Chalmers University of Technology)\n<\/p>\n
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\nAbstract:<\/strong>
\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.
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