Coupled equations for Kähler metrics and YangMills connections (Thesis)
Abstract
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 HermiteYangMills 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 Kenergy. We explain their relationship to the algebrogeometric moduli problem for pairs consisting of a polarized variety and a holomorphic vector bundle.
 Publication:

arXiv eprints
 Pub Date:
 February 2011
 arXiv:
 arXiv:1102.0985
 Bibcode:
 2011arXiv1102.0985G
 Keywords:

 Mathematics  Differential Geometry;
 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Mathematics  Symplectic Geometry
 EPrint:
 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