Coupled equations for K\"ahler metrics and Yang-Mills connections   (Thesis)
  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. 
Mario Garcia-Fernandez
math.DG math-ph math.AG math.MP math.SG