Universiteit Leiden Mathematisch Instituut
Geometry Seminar

Wednesday, 2 April 2003, 16:00 - 17:00, room 403

Mihai Sorin Stupariu: The Kobayashi-Hitchin correspondence

Abstract:

In the previous talk we described the relationship between some objects constructed in the algebraic geometry (GIT-Quotients) and certain quotients which arise in the symplectic geometry. Today we will present a result which is an infinite dimensional analogous and which establishes a link between algebraic and differential geometry.

Let E be a differentiable complex vector bundle over a compact Kähler manifold. On one hand, one can construct the moduli space of isomorphism classes of stable holomorphic structures in E. We notice that the notion of stability used has its origin in the algebraic geometry. On the other hand, fixing a Hermitian metric in E, one obtains the moduli space of gauge-equivalence classes of unitary Hermitian-Einstein connections in E, which arises in the differential geometry. The aim of the talk is to describe the natural 1:1 correspondence between these two moduli spaces.