Compatible Poisson Brackets Associated with Elliptic Curves in $G(2,5)$
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Published:2024-05-07
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ISSN:1815-0659
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Container-title:Symmetry, Integrability and Geometry: Methods and Applications
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Short-container-title:SIGMA
Author:
,Markarian Nikita, , ,Polishchuk Alexander,
Abstract
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 $G(2,5)$.
Publisher
SIGMA (Symmetry, Integrability and Geometry: Methods and Application)