Space of initial conditions for the four-dimensional Garnier system revisited
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914911665258496 |
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| author | Takenawa, Tomoyuki |
| author_facet | Takenawa, Tomoyuki |
| contents | A geometric study is given for the 4-dimensional Garnier system. By the resolution of indeterminacy, the group of its Bäklund transformations is lifted to a group of pseudo-isomorphisms between rational varieties obtained from ${\mathbb P}^2 \times {\mathbb P}^2$ by 10 or 21 blow-ups. The root basis is discussed in the Néron-Severi bilattices for the space with 10 blow-ups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_00993 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Space of initial conditions for the four-dimensional Garnier system revisited Takenawa, Tomoyuki Algebraic Geometry Dynamical Systems 37F10, 34M55, 14E07 A geometric study is given for the 4-dimensional Garnier system. By the resolution of indeterminacy, the group of its Bäklund transformations is lifted to a group of pseudo-isomorphisms between rational varieties obtained from ${\mathbb P}^2 \times {\mathbb P}^2$ by 10 or 21 blow-ups. The root basis is discussed in the Néron-Severi bilattices for the space with 10 blow-ups. |
| title | Space of initial conditions for the four-dimensional Garnier system revisited |
| topic | Algebraic Geometry Dynamical Systems 37F10, 34M55, 14E07 |
| url | https://arxiv.org/abs/2404.00993 |