nLab
Kobayashi-Hitchin correspondence

Contents

Context

Differential cohomology

Complex geometry

Contents

Idea

The Kobayashi-Hitchin correspondence states that over suitable complex manifolds the moduli space of semi-stable vector bundles and that of Hermite-Einstein connections are essentially the same.

For the special case over Kähler manifolds this is the Donaldson-Uhlenbeck-Yau theorem. For the special case over Riemann surfaces it is the Narasimhan-Seshadri theorem. See also Deligne’s characterization of intermediate Jacobians (in particular there at Examples – Picard variety).

References

Last revised on October 3, 2018 at 16:05:07. See the history of this page for a list of all contributions to it.