Remarks on Higgs bundles twisted by a vector bundle
Algebraic Geometry
2025-06-10 v1
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.
Cite
@article{arxiv.2506.06573,
title = {Remarks on Higgs bundles twisted by a vector bundle},
author = {David Alfaya and Indranil Biswas and Pradip Kumar},
journal= {arXiv preprint arXiv:2506.06573},
year = {2025}
}
Comments
10 pages