Dynamical systems on some elliptic modular surfaces via operators on line arrangements
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908694487236608 |
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| author | Kühne, Lukas Roulleau, Xavier |
| author_facet | Kühne, Lukas Roulleau, Xavier |
| contents | This paper further studies the matroid realization space of a specific deformation of the regular $n$-gon with its lines of symmetry. Recently, we obtained that these particular realization spaces are birational to the elliptic modular surfaces $Ξ_{1}(n)$ over the modular curve $X_1(n)$. Here, we focus on the peculiar cases when $n=7,8$ in more detail. We obtain concrete quartic surfaces in $\mathbb{P}^3$ equipped with a dominant rational self-map stemming from an operator on line arrangements, which yields K3 surfaces with a dynamical system that is semi-conjugated to the plane. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18207 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical systems on some elliptic modular surfaces via operators on line arrangements Kühne, Lukas Roulleau, Xavier Algebraic Geometry Dynamical Systems 14N20, 14H50, 37D40 This paper further studies the matroid realization space of a specific deformation of the regular $n$-gon with its lines of symmetry. Recently, we obtained that these particular realization spaces are birational to the elliptic modular surfaces $Ξ_{1}(n)$ over the modular curve $X_1(n)$. Here, we focus on the peculiar cases when $n=7,8$ in more detail. We obtain concrete quartic surfaces in $\mathbb{P}^3$ equipped with a dominant rational self-map stemming from an operator on line arrangements, which yields K3 surfaces with a dynamical system that is semi-conjugated to the plane. |
| title | Dynamical systems on some elliptic modular surfaces via operators on line arrangements |
| topic | Algebraic Geometry Dynamical Systems 14N20, 14H50, 37D40 |
| url | https://arxiv.org/abs/2402.18207 |