Stratifying moduli spaces of Higgs bundles and the Hitchin morphism
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918286083489792 |
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| author | Patel, Aryaman Weissmann, Dario |
| author_facet | Patel, Aryaman Weissmann, Dario |
| contents | 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-étale cover. Fixing the rank, there is one quasi-étale 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-Ngô's conjecture holds for hyperelliptic varieties in characteristic $0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_08597 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stratifying moduli spaces of Higgs bundles and the Hitchin morphism Patel, Aryaman Weissmann, Dario Algebraic Geometry 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-étale cover. Fixing the rank, there is one quasi-étale 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-Ngô's conjecture holds for hyperelliptic varieties in characteristic $0$. |
| title | Stratifying moduli spaces of Higgs bundles and the Hitchin morphism |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2601.08597 |