Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Singularities of Hermitian-Yang-Mills connections and reflexive sheaves


Speaker: Song Sun, UC Berkeley
Related Webpage:
Location: 2112 MSB
Start time: Thu, May 10 2018, 1:10PM

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. If time permits I will discuss an interesting related algebro-geometric construction. This talk is based on joint work with Xuemiao Chen.

This is a joint seminar in algebraic geometry and geometry/topology.