Invariant vector bundles and Hitchin systems

Zakaria Ouaras; Hacen Zelaci

Invariant vector bundles and Hitchin systems

Algebraic Geometry 2025-04-09 v1

Authors: Zakaria Ouaras , Hacen Zelaci

Abstract

Let $X\rightarrow Y$ be a Galois cover with Galois group $\Gamma$ , where $X$ and $Y$ are smooth complex projective curve of genus $\geqslant 2$ . In this paper, we study the moduli spaces of semistable $\Gamma-$ invariant vector bundles on $X$ and classify their connected components. We also study the Hitchin systems on these moduli spaces and determine their fibers in the smooth case.

Keywords

higgs bundle moduli spaces of vector bundles vector bundles

Cite

@article{arxiv.2504.05440,
  title  = {Invariant vector bundles and Hitchin systems},
  author = {Zakaria Ouaras and Hacen Zelaci},
  journal= {arXiv preprint arXiv:2504.05440},
  year   = {2025}
}

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