On diagonal pluriharmonic metrics of G-Higgs bundles

Natsuo Miyatake ()
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Natsuo Miyatake: Tohoku University

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 4, 1285-1289

Abstract: Abstract Let $$(E,\Phi )\rightarrow (X,\omega _X)$$ ( E , Φ ) → ( X , ω X ) be a Higgs bundle over a compact Kähler 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.

Keywords: Higgs bundle; Harmonic bundle; Stability condition; Torus action (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00434-x

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