Compatible Poisson brackets associated with elliptic curves in $G(2,5)$

Author:

Nikita Markarian, Alexander Polishchuk

Keyword:

Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG)

journal:

date:

2023-10-27 16:00:00

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 $G(2,5)$.

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