Compatible Poisson Brackets Associated with Elliptic Curves in (2,5)
We prove that a pair of Feigin-Odesskii Poisson brackets on ℙ⁴ associated with elliptic curves given as linear sections of the Grassmannian (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 (2,5).
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2024 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2024
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/212158 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Compatible Poisson Brackets Associated with Elliptic Curves in (2,5). Nikita Markarian and Alexander Polishchuk. SIGMA 20 (2024), 037, 19 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862718913938194432 |
|---|---|
| author | Markarian, Nikita Polishchuk, Alexander |
| author_facet | Markarian, Nikita Polishchuk, Alexander |
| citation_txt | Compatible Poisson Brackets Associated with Elliptic Curves in (2,5). Nikita Markarian and Alexander Polishchuk. SIGMA 20 (2024), 037, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove that a pair of Feigin-Odesskii Poisson brackets on ℙ⁴ associated with elliptic curves given as linear sections of the Grassmannian (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 (2,5).
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| first_indexed | 2026-03-20T21:57:14Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212158 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-20T21:57:14Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Markarian, Nikita Polishchuk, Alexander 2026-01-30T08:13:30Z 2024 Compatible Poisson Brackets Associated with Elliptic Curves in (2,5). Nikita Markarian and Alexander Polishchuk. SIGMA 20 (2024), 037, 19 pages 1815-0659 2020 Mathematics Subject Classification: 14H52; 53D17 arXiv:2310.18759 https://nasplib.isofts.kiev.ua/handle/123456789/212158 https://doi.org/10.3842/SIGMA.2024.037 We prove that a pair of Feigin-Odesskii Poisson brackets on ℙ⁴ associated with elliptic curves given as linear sections of the Grassmannian (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 (2,5). We are grateful to Volodya Rubtsov for useful discussions and to the anonymous referee for helpful comments. N.M. would like to thank the Max Planck Institute for Mathematics for its hospitality and perfect work conditions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Compatible Poisson Brackets Associated with Elliptic Curves in (2,5) Article published earlier |
| spellingShingle | Compatible Poisson Brackets Associated with Elliptic Curves in (2,5) Markarian, Nikita Polishchuk, Alexander |
| title | Compatible Poisson Brackets Associated with Elliptic Curves in (2,5) |
| title_full | Compatible Poisson Brackets Associated with Elliptic Curves in (2,5) |
| title_fullStr | Compatible Poisson Brackets Associated with Elliptic Curves in (2,5) |
| title_full_unstemmed | Compatible Poisson Brackets Associated with Elliptic Curves in (2,5) |
| title_short | Compatible Poisson Brackets Associated with Elliptic Curves in (2,5) |
| title_sort | compatible poisson brackets associated with elliptic curves in (2,5) |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212158 |
| work_keys_str_mv | AT markariannikita compatiblepoissonbracketsassociatedwithellipticcurvesin25 AT polishchukalexander compatiblepoissonbracketsassociatedwithellipticcurvesin25 |