Coupled K\"ahler-Einstein and Hermitian-Yang-Mills equations

Kartick Ghosh

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arXiv · 2212.01043

Coupled K\"ahler-Einstein and Hermitian-Yang-Mills equations

Kartick Ghosh

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Abstract

We introduce a new system of equations coupling K\"ahler-Einstein and Hermitian-Yang-Mills equations. We provide a moment map interpretation of these equations. We identify a Futaki type invariant as an obstruction to the existence of solutions to these equations. We also prove a Matsushima-Lichnerowicz type theorem. We prove a deformation result that produces nontrivial solutions of these equations under some conditions. We produce examples on some projective bundles using Calabi ansatz.

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Kartick Ghosh. 2022-12-02. Coupled K\"ahler-Einstein and Hermitian-Yang-Mills equations. https://arxiv.org/abs/2212.01043

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