Segre surfaces and geometry of the Painlevé equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914409472851968 |
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| author | Joshi, Nalini Mazzocco, Marta Roffelsen, Pieter |
| author_facet | Joshi, Nalini Mazzocco, Marta Roffelsen, Pieter |
| contents | In this paper, we consider a six parameter family of affine Segre surfaces embedded in $\mathbb C^6$. For generic values of the parameters, this family is associated to the $q$-difference sixth Painlevé equation. We show that different limiting forms of this family give Segre surfaces that are isomorphic as affine varieties to the the monodromy manifolds of each Painlevé differential equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_10541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Segre surfaces and geometry of the Painlevé equations Joshi, Nalini Mazzocco, Marta Roffelsen, Pieter Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems 34M55, 39A13, 14J10 In this paper, we consider a six parameter family of affine Segre surfaces embedded in $\mathbb C^6$. For generic values of the parameters, this family is associated to the $q$-difference sixth Painlevé equation. We show that different limiting forms of this family give Segre surfaces that are isomorphic as affine varieties to the the monodromy manifolds of each Painlevé differential equation. |
| title | Segre surfaces and geometry of the Painlevé equations |
| topic | Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems 34M55, 39A13, 14J10 |
| url | https://arxiv.org/abs/2405.10541 |