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arXiv · 2504.05440

Invariant vector bundles and Hitchin systems

Zakaria Ouaras·Hacen Zelaci
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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.

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Zakaria Ouaras, Hacen Zelaci. 2025-04-07. Invariant vector bundles and Hitchin systems. https://arxiv.org/abs/2504.05440

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