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

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.


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