Moduli of extensions of holomorphic bundles on Kähler manifolds. (English) Zbl 0852.58014

Daskalopoulos, Georgios; Uhlenbeck, Karen; Wentworth, Richard

Commun. Anal. Geom. 3, No. 3, 479-522 (1995).

This paper considers extended Hermitian-Einstein equations on a compact Kähler manifold, presenting a description of the space of equivalence classes of solutions. Holomorphic extension pairs associated to the equations are described, as is a notion of stability of such pairs. A gauge-theoretic construction of the moduli space of the pairs is given and it is shown generically to have a Kähler manifold structure. The moduli space is also constructed via geometric invariant theory when the underlying manifold is algebraic.

Reviewer: D.B.Gauld (Auckland)

MSC:

58D27	Moduli problems for differential geometric structures
32Q20	Kähler-Einstein manifolds
81T13	Yang-Mills and other gauge theories in quantum field theory

Keywords:

Hermitian-Einstein equations; Kähler manifold; moduli space