QGM Seminar by Yoshinori Hashimoto (Tokyo Institute of Technology)

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

2019.01.09 | Jane Jamshidi

Date Fri 01 Feb
Time 14:15 15:15
Location 1530-326


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.