Moduli of extensions of holomorphic bundles on Kähler manifolds (Q1911810)

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.