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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2401.09956 |
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| _version_ | 1866917590699343872 |
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| author | Sheng, Mao Sun, Hao Wang, Jianping |
| author_facet | Sheng, Mao Sun, Hao Wang, Jianping |
| contents | In this paper, we study the existence of gr-semistable filtrations of orthogonal/symplectic $λ$-connections. It is known that gr-semistable filtrations always exist for flat bundles in arbitrary characteristic. However, we found a counterexample of orthogonal flat bundles of rank 5 in positive characteristic. The central new idea in this example is the notion of quasi gr-semistability for orthogonal/symplectic $λ$-connections. We establish the equivalence between gr-semistability and quasi gr-semistablity for an orthogonal/symplectic $λ$-connection. This provides a way to determine whether an orthogonal/symplectic $λ$-connection is gr-semistable. As an application, we obtain a characterization of gr-semistable orthogonal $λ$-connections of rank $\leq 6$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09956 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Existence of Gr-semistable Filtrations of Orthogonal/Symplectic $λ$-connections Sheng, Mao Sun, Hao Wang, Jianping Algebraic Geometry 14D07, 14J60 In this paper, we study the existence of gr-semistable filtrations of orthogonal/symplectic $λ$-connections. It is known that gr-semistable filtrations always exist for flat bundles in arbitrary characteristic. However, we found a counterexample of orthogonal flat bundles of rank 5 in positive characteristic. The central new idea in this example is the notion of quasi gr-semistability for orthogonal/symplectic $λ$-connections. We establish the equivalence between gr-semistability and quasi gr-semistablity for an orthogonal/symplectic $λ$-connection. This provides a way to determine whether an orthogonal/symplectic $λ$-connection is gr-semistable. As an application, we obtain a characterization of gr-semistable orthogonal $λ$-connections of rank $\leq 6$. |
| title | On the Existence of Gr-semistable Filtrations of Orthogonal/Symplectic $λ$-connections |
| topic | Algebraic Geometry 14D07, 14J60 |
| url | https://arxiv.org/abs/2401.09956 |