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

Presented by: 
Song Sun Stony Brook University
Thursday 17th August 2017 - 14:00 to 15:00
INI Seminar Room 1
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. 

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons