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Compatible Poisson Brackets Associated with Elliptic Curves in $G(2,5)$
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $G(2,5)$.
Keywords: bi-Hamiltonian structure, elliptic curve, triple Massey products.
Mots-clés : Poisson bracket 
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     title = {Compatible {Poisson} {Brackets} {Associated} with {Elliptic} {Curves} in $G(2,5)$},
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Nikita Markaryan; Alexander Polishchuk. Compatible Poisson Brackets Associated with Elliptic Curves in $G(2,5)$. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a36/

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