Singularities of Hermitian-Yang-Mills connections and the Harder-Narasimhan-Seshadri filtration
1 hour 6 mins,
964.17 MB,
MPEG-4 Video
640x360,
29.97 fps,
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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) |
Distribution: | World (downloadable) |
Explicit content: | No |
Aspect Ratio: | 16:9 |
Screencast: | No |
Bumper: | UCS Default |
Trailer: | UCS Default |
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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