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Restriction of Donaldson's functional to diagonal metrics on Higgs bundles with non-holomorphic Higgs fields | Natsuo Miyatake
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4 Jan 2023 | Abstract: | We consider a Higgs bundle over a compact Kähler manifold with a smooth,
non-holomorphic Higgs field. We assume that the holomorphic vector bundle
decomposes into a direct sum of holomorphic line bundles. Under an assumption
on the non-holomorphic Higgs field, we provide some necessary and sufficient
conditions for Donaldson’s functional to attain a minimum at the set of
diagonal Hermitian metrics for the decomposition of the vector bundle. In
particular, we show that we can solve the Hermitian-Einstein equation under a
strong assumption even if the Higgs field is non-holomorphic. | Source: | arXiv, 2301.01485 | Services: | Forum | Review | PDF | Favorites |
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