Compatible Poisson Brackets Associated with Elliptic Curves in $G(2,5)$
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914786422292480 |
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| author | Markarian, Nikita Polishchuk, Alexander |
| author_facet | Markarian, Nikita Polishchuk, Alexander |
| contents | We prove that a pair of Feigin-Odesskii Poisson brackets on ${\mathbb P}^4$ associated with elliptic curves given as linear sections of the Grassmannian $G(2,5)$ are compatible if and only if this pair of elliptic curves is contained in a del Pezzo surface obtained as a linear section of $G(2,5)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_18759 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Compatible Poisson Brackets Associated with Elliptic Curves in $G(2,5)$ Markarian, Nikita Polishchuk, Alexander Algebraic Geometry We prove that a pair of Feigin-Odesskii Poisson brackets on ${\mathbb P}^4$ associated with elliptic curves given as linear sections of the Grassmannian $G(2,5)$ are compatible if and only if this pair of elliptic curves is contained in a del Pezzo surface obtained as a linear section of $G(2,5)$. |
| title | Compatible Poisson Brackets Associated with Elliptic Curves in $G(2,5)$ |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2310.18759 |