Singularities of Hermitian-Yang-Mills connections and the Harder-Narasimhan-Seshadri filtration
Duration: 1 hour 6 mins
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About this item
| Description: |
Sun, S
Thursday 17th August 2017 - 14:00 to 15:00 |
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| Created: | 2017-08-18 09:02 |
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| Collection: | Symplectic geometry - celebrating the work of Simon Donaldson |
| Publisher: | Isaac Newton Institute |
| Copyright: | Sun, S |
| Language: | eng (English) |
| Abstract: | 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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