We study equations on a principal bundle over a compact complex manifold coupling connections on the bundle with Kähler structures in the base. These equations generalize the conditions of constant scalar curvature for a Kähler metric and Hermite-Yang-Mills for a connection. We provide a moment map interpretation of the equations and study obstructions for the existence of solutions, generalizing the Futaki character and the Mabuchi K-energy. We explain their relationship to the algebro-geometric moduli problem for pairs consisting of a polarized variety and a holomorphic vector bundle.
- Pub Date:
- February 2011
- Mathematics - Differential Geometry;
- Mathematical Physics;
- Mathematics - Algebraic Geometry;
- Mathematics - Symplectic Geometry
- 120 pages. More general formula for the moment map, which includes a twist by an element in the centre of the Lie algebra of the structure group