Compatible quadratic Poisson brackets related to a family of elliptic curves

Abstract

We construct nine pairwise compatible quadratic Poisson structures such that a generic linear combination of them is associated with an elliptic algebra in n generators. Explicit formulas for Casimir elements of this elliptic Poisson structure are obtained.

arXiv comment17 pages, Latex, major changes

References in corpus (1)

• Webs, Lenard schemes, and the local geometry of bihamiltonian Toda and Lax structures

Cited by in corpus (5)

• Feigin-Odesskii brackets, syzygies, and Cremona transformations
• Ten Compatible Poisson Brackets on ${\mathbb{P}}^5$
• Compatible Poisson Brackets Associated with Elliptic Curves in $G(2,5)$
• Elliptic bihamiltonian structures from relative shifted Poisson structures
• Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets