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- W4313598316 abstract "We consider a Higgs bundle over a compact Kahler 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 zero set of the non-holomorphic Higgs field, we provide some necessary and sufficient conditions for Donaldson's functional which is restricted to the set of diagonal Hermitian metrics associated with a holomorphic decomposition of the vector bundle to attain a minimum. In particular, when the holomorphic vector bundle decomposes into a direct sum of holomorphic line bundles, we show that we can solve the Hermitian-Einstein equation under a strong assumption even if the Higgs field is non-holomorphic." @default.
- W4313598316 created "2023-01-06" @default.
- W4313598316 creator A5074507942 @default.
- W4313598316 date "2023-01-04" @default.
- W4313598316 modified "2023-09-28" @default.
- W4313598316 title "Restriction of Donaldson's functional to diagonal metrics on Higgs bundles with non-holomorphic Higgs fields" @default.
- W4313598316 doi "https://doi.org/10.48550/arxiv.2301.01485" @default.
- W4313598316 hasPublicationYear "2023" @default.
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