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Variational approach to the Kobayashi-Hitchin correspondence and the Quot-scheme limits

Yoshinori Hashimoto (Tokyo Institute of Technology)
Friday, 1 February, 2019, at 14:15-15:15, in Aud. D3 (1531-215)
The Kobayashi-Hitchin correspondence states that the existence of Hermitian-Einstein metrics on a holomorphic vector bundle is equivalent to an algebro-geometric stability condition, and was proved by Donaldson and Uhlenbeck-Yau. Their original proofs were based on technical and sophisticated applications of nonlinear PDE theory. We present some results that clarify variational aspects of the Kobayashi--Hitchin correspondence for smooth projective varieties; they are based on the theory of Quot-schemes in algebraic geometry and rely much less on analysis. Joint work with Julien Keller.
Organised by: QGM
Contact person: Cristiano Spotti