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Singularities of Hermitian-Yang-Mills connections and the Harder-Narasimhan-Seshadri filtration

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SYGW05 - Symplectic geometry - celebrating the work of Simon Donaldson

Co-Author: Xuemiao Chen (Stony Brook)

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 part of the Isaac Newton Institute Seminar Series series.

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