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

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 $G(2,5)$.

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Bibliographic Details
Published inSymmetry, integrability and geometry, methods and applications
Main Authors Markarian, Nikita, Polishchuk, Alexander
Format Journal Article
LanguageEnglish
Published National Academy of Science of Ukraine 07.05.2024
Subjects
Algebraic Geometry
Mathematics
Poisson bracket
triple Massey products 2020 Mathematics Subject Classification: 14H52
elliptic curve
bi-Hamiltonian structure
Poisson bracket bi-Hamiltonian structure elliptic curve triple Massey products 2020 Mathematics Subject Classification: 14H52 53D17
53D17
Online AccessGet full text
ISSN1815-0659
1815-0659
DOI10.3842/SIGMA.2024.037

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Summary: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 $G(2,5)$.
ISSN:1815-0659
1815-0659
DOI:10.3842/SIGMA.2024.037