Compatible Poisson Brackets Associated with Elliptic Curves in (2,5)

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• Main Authors: Markarian, Nikita, Polishchuk, Alexander
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212158
• 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

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).