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).
Wikipedia, Kobayashi-Hitchin correspondence
Shoshichi Kobayashi, Differential geometry of complex vector bundles, Princeton University Press (1987) (pdf)
Martin Lübke?, and Andrei Teleman?, The Kobayashi-Hitchin correspondence, World Scientific, 1995.
Last revised on October 3, 2018 at 20:05:07. See the history of this page for a list of all contributions to it.