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arXiv · 2111.07330

On diagonal pluriharmonic metrics of $G$-Higgs bundles

Natsuo Miyatake
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Abstract

Let $(E,\Phi)\rightarrow (X,\omega_X)$ be a Higgs bundle over a compact K\"ahler manifold. We suppose that the holomorphic vector bundle $E$ decomposes into a direct sum of holomorphic line bundles. In this paper, we give the necessary and sufficient condition for the existence of a diagonal metric which is a solution to the Hermitian-Einstein equation. Our theorem can easily be generalized to $G$-Higgs bundles. We also describe the relationship between the stability condition and our condition using the torus action on the space of Higgs fields.

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Natsuo Miyatake. 2021-11-14. On diagonal pluriharmonic metrics of $G$-Higgs bundles. https://doi.org/10.1007/s13226-023-00434-x

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