Coble surfaces: projective models and automorphisms with related topics
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911548138586112 |
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| author | Pieroni, Federico |
| author_facet | Pieroni, Federico |
| contents | In this work, we want to show several properties of an unnodal, complex Coble surface $X$ with irreducible boundary curve $C \in |-2 K_X|$. Namely, we show that every isotropic sequence ${\cal E}_1, \ldots, {\cal E}_r$ with $r \le 8$ and ${\cal E}_i {\cal E}_j = 1 - δ_{i, j}$ can be extended to a sequence of length $10$. Moreover, such a surface admits a birational quintic model $\overline X \subset \mathbb{P}^3$, with equation $αX_0 X_1^2 X_2^2 + βX_0 X_1^2 X_3^2 + γX_0 X_2^2 X_3^2 + X_1 X_2 X_3 q = 0$, where $q$ is a quadric form. Finally, we use this birational model to show that every biregular involution $i : X \to X$ on such a Coble surface is the lift of a Bertini involution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_26338 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coble surfaces: projective models and automorphisms with related topics Pieroni, Federico Algebraic Geometry In this work, we want to show several properties of an unnodal, complex Coble surface $X$ with irreducible boundary curve $C \in |-2 K_X|$. Namely, we show that every isotropic sequence ${\cal E}_1, \ldots, {\cal E}_r$ with $r \le 8$ and ${\cal E}_i {\cal E}_j = 1 - δ_{i, j}$ can be extended to a sequence of length $10$. Moreover, such a surface admits a birational quintic model $\overline X \subset \mathbb{P}^3$, with equation $αX_0 X_1^2 X_2^2 + βX_0 X_1^2 X_3^2 + γX_0 X_2^2 X_3^2 + X_1 X_2 X_3 q = 0$, where $q$ is a quadric form. Finally, we use this birational model to show that every biregular involution $i : X \to X$ on such a Coble surface is the lift of a Bertini involution. |
| title | Coble surfaces: projective models and automorphisms with related topics |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2603.26338 |