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Singularities of Hermitian-Yang-Mills connections and reflexive sheaves
Algebraic Geometry and Number Theory| Speaker: | Song Sun, UC Berkeley |
| Related Webpage: | http://www.math.stonybrook.edu/~ssun/ |
| 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.