Colloquium | Institute of Mathematical Sciences
Time：16:00-17:00, June 20, Thursday
Location：Room S407, IMS
Speaker: Song Sun, UC Berkeley
Abstract: The Donaldson-Uhlenbeck-Yau theorem relates the existence of Hermitian-Yang-Mills connection over a compact Kahler manifold with algebraic stability of a holomorphic vector bundle. This has been extended by Bando-Siu to the case of reflexive sheaves, and the corresponding connection may have singularities. We study tangent cones around such a singularity, which is defined in the usual geometric analytic way, and relate it to the Harder-Narasimhan-Seshadri filtration of a suitably defined torsion free sheaf on the projective space, which is a purely algebro-geometric object. This talk is based on joint works with Xuemiao Chen.