Semiprojectivity and very stability in moduli of symplectic and orthogonal parabolic Higgs bundles
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866912977439948800 |
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| author | Roy, Sumit |
| author_facet | Roy, Sumit |
| contents | Let $X$ be a compact Riemann surface of genus $g \geq 2$, and let $D \subset X$ be a fixed finite subset. We prove the semiprojectivity of the moduli space of semistable symplectic or orthogonal parabolic Higgs bundles over $X$. We show that a stable symplectic parabolic bundle $E$ on $X$ is strongly very stable, meaning $E$ does not have any nonzero strongly parabolic nilpotent Higgs field, if and only if the symplectic parabolic Hitchin morphism induced on the affine space $$H^0(X,\mathrm{SPEnd}_\mathrm{Sp}(E) \otimes K(D))$$ is a proper morphism, where $\mathrm{SPEnd}_\mathrm{Sp}(E)$ denotes the set of symplectic strongly parabolic endomorphisms of $E$. We remark that the same criterion for very stability applies to the orthogonal case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20915 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Semiprojectivity and very stability in moduli of symplectic and orthogonal parabolic Higgs bundles Roy, Sumit Algebraic Geometry 14D20, 14H60, 14H70 Let $X$ be a compact Riemann surface of genus $g \geq 2$, and let $D \subset X$ be a fixed finite subset. We prove the semiprojectivity of the moduli space of semistable symplectic or orthogonal parabolic Higgs bundles over $X$. We show that a stable symplectic parabolic bundle $E$ on $X$ is strongly very stable, meaning $E$ does not have any nonzero strongly parabolic nilpotent Higgs field, if and only if the symplectic parabolic Hitchin morphism induced on the affine space $$H^0(X,\mathrm{SPEnd}_\mathrm{Sp}(E) \otimes K(D))$$ is a proper morphism, where $\mathrm{SPEnd}_\mathrm{Sp}(E)$ denotes the set of symplectic strongly parabolic endomorphisms of $E$. We remark that the same criterion for very stability applies to the orthogonal case. |
| title | Semiprojectivity and very stability in moduli of symplectic and orthogonal parabolic Higgs bundles |
| topic | Algebraic Geometry 14D20, 14H60, 14H70 |
| url | https://arxiv.org/abs/2603.20915 |