English

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.

Keywords

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

R2 v1 2026-07-01T03:04:31.637Z