Geometric Analysis Seminar——Algebraicity of metric tangent cones and equivariant K-stability
主 题: Geometric Analysis Seminar——Algebraicity of metric tangent cones and equivariant K-stability
报告人: Prof. Chi Li (Purdue University)
时 间: 2018-05-08 10:00-11:00
地 点: Room 1303, Sciences Building No. 1
Abstract: Donaldson-Sun conjectured that the metric tangent cone at any point on a Gromov-Hausdorff (GH) limit of Kahler-Einstein Fano manifolds depends only on the algebraic structure of the GH limit. I will explain a proof of this conjecture. The proof depends on the characterization of K-semistable Fano cones via minimizers of normalized volumes, and proving uniqueness of K-polystable degenerations for K-semistable Fano cones. We also prove that to test K-stability of a Fano T-variety (possibly singular), it is sufficient to test on T-equivariant special test configurations. This is based on joint works with Xiaowei Wang and Chenyang Xu.