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Coupled equations for Khler metrics and Yang-Mills connections

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Moduli Spaces

We study equations on a principal bundle over a compact complex manifold coupling a connection on the bundle with a Khler structure on the base. These equations generalize the conditions of constant scalar curvature for a Khler 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 invariant, the Mabuchi K-energy and geodesic stability. We finish by giving some examples of solutions. This is joint work with Mario Garcia-Fernandez and Oscar Garcia-Prada (arXiv:1102.0991 [math.DG]).

This talk is part of the Isaac Newton Institute Seminar Series series.

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