Invariant vector bundles and Hitchin systems

2025/04/07 by Zakaria Ouaras, Ouaras, Zakaria, Hacen Zelaci +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2504.05440

openalex publication_date 2025/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X→ Y be a Galois cover with Galois group Γ, where X and Y are smooth complex projective curve of genus \geqslant 2. In this paper, we study the moduli spaces of semistable Γ-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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