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

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 $G(2,5)$.

References in corpus (1)

• Ten Compatible Poisson Brackets on ${\mathbb{P}}^5$

Cited by in corpus (1)

• On Conormal Lie Algebras of Feigin-Odesskii Poisson Structures