不变向量束与Hitchin系统

IF 0.9 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2025-06-20 DOI:10.1016/j.bulsci.2025.103687

Zakaria Ouaras , Hacen Zelaci

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引用次数: 0

摘要

设X→Y是具有伽罗瓦群Γ的伽罗瓦覆盖，其中X和Y是属小于或等于2的光滑复投影曲线。本文研究了X上半稳定Γ-invariant向量束的模空间，并对它们的连通分量进行了分类。我们还研究了这些模空间上的Hitchin系统，并确定了它们在光滑情况下的纤维。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Invariant vector bundles and Hitchin systems

Let

X \to Y

be a Galois cover with Galois group Γ, where X and Y are smooth complex projective curve of genus ⩾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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