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arXiv · 2506.06573

Remarks on Higgs bundles twisted by a vector bundle

David Alfaya·Indranil Biswas·Pradip Kumar
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Abstract

For any V-twisted Higgs bundle on a compact Riemann surface X, where V is a holomorphic vector bundle of rank two on X, there are two associated Higgs bundles on X, twisted by line bundles, which are constructed using a Hecke transformation on V. We characterize all such pairs of Higgs bundles (twisted by line bundles) given by V-twisted Higgs bundles. Using this characterization, we provide a spectral correspondence for the moduli space, identifying V-twisted Higgs bundles with the direct images of certain rank one torsionfree Higgs sheaves twisted by a line bundle on a spectral covering of the curve X.

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David Alfaya, Indranil Biswas, Pradip Kumar. 2025-06-06. Remarks on Higgs bundles twisted by a vector bundle. https://arxiv.org/abs/2506.06573

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