Coupled equations for K\"ahler metrics and Yang-Mills connections (Thesis)
Differential Geometry
2011-09-23 v2 Mathematical Physics
Algebraic Geometry
math.MP
Symplectic Geometry
Abstract
We study equations on a principal bundle over a compact complex manifold coupling connections on the bundle with K\"ahler structures in the base. These equations generalize the conditions of constant scalar curvature for a K\"ahler 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.
Keywords
Cite
@article{arxiv.1102.0985,
title = {Coupled equations for K\"ahler metrics and Yang-Mills connections (Thesis)},
author = {Mario Garcia-Fernandez},
journal= {arXiv preprint arXiv:1102.0985},
year = {2011}
}
Comments
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