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arXiv · 1807.10691

On the K\"ahler-Yang-Mills-Higgs equations

Luis Álvarez-Cónsul·Mario Garcia-Fernandez·Oscar García-Prada
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Abstract

In this paper we introduce a set of equations on a principal bundle over a compact complex manifold coupling a connection on the principal bundle, a section of an associated bundle with K\"ahler fibre, and a K\"ahler structure on the base. These equations are a generalization of the K\"ahler-Yang-Mills equations introduced by the authors. They also generalize the constant scalar curvature for a K\"ahler metric studied by Donaldson and others, as well as the Yang-Mills-Higgs equations studied by Mundet i Riera. We provide a moment map interpretation of the equations, construct some first examples, and study obstructions to the existence of solutions.

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Luis Álvarez-Cónsul, Mario Garcia-Fernandez, Oscar García-Prada. 2018-07-27. On the K\"ahler-Yang-Mills-Higgs equations. https://arxiv.org/abs/1807.10691

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