Stratifying moduli spaces of Higgs bundles and the Hitchin morphism

Aryaman Patel; Dario Weissmann

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arXiv · 2601.08597

Stratifying moduli spaces of Higgs bundles and the Hitchin morphism

Aryaman Patel·Dario Weissmann

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Abstract

We study the behavior of slope-stability of reflexive twisted sheaves over a normal projective variety $X$ under pullback along a cover. Slope-stability is always preserved if the cover does not factor via a quasi-\'etale cover. Fixing the rank, there is one quasi-\'etale cover that checks whether a twisted sheaf remains slope-stable on all Galois covers, yielding a stratification of the moduli space of slope-stable Higgs-bundles. As an application, we determine the image of the Hitchin morphism restricted to the smallest closed stratum of the Dolbeault moduli space when $X$ is smooth. This allows us to determine the image of the Hitchin morphism from the Dolbeault moduli space when $X$ is a hyperelliptic or abelian variety in characteristic $p\ge0$. In particular, we show that Chen-Ng\^o's conjecture holds for hyperelliptic varieties in characteristic $0$.

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Aryaman Patel, Dario Weissmann. 2026-01-13. Stratifying moduli spaces of Higgs bundles and the Hitchin morphism. https://arxiv.org/abs/2601.08597

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