Singular Hermitian-Yang-Mills connections and reflexive sheaves


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December 6, 2019 3:30 pm - 4:30 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

Song Sun - Berkeley

The Donaldson-Uhlenbeck-Yau theorem relates the existence of Hermitian-Yang-Mills connections over a compact Kahler manifold with algebraic stability of a holomorphic vector bundle. This has been extended by Bando-Siu in 1994 to a class of singular Hermitian-Yang-Mills connections on reflexive sheaves. We study tangent cones of these singular connections in the geometric analytic sense, and show that they can be characterized in terms of certain algebro-geometric invariants of reflexive sheaves. In a sense, this can be viewed as a "local" version of the Donaldson-Uhlenbeck-Yau correspondence.  Based on joint work with Xuemiao Chen (University of Maryland). 

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