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16 February 2025
 
  » arxiv » 2301.01485

 Article overview



Restriction of Donaldson's functional to diagonal metrics on Higgs bundles with non-holomorphic Higgs fields
Natsuo Miyatake ;
Date 4 Jan 2023
AbstractWe 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
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