The symplectic leaves for the elliptic Poisson bracket on projective space defined by Feigin-Odesskii and Polishchuk

This paper determines the symplectic leaves for a remarkable Poisson structure on CPⁿ⁻¹ discovered by Feigin and Odesskii, and, independently, by Polishchuk. The Poisson bracket is determined by a holomorphic line bundle of degree n ≥ 3 on a compact Rie-mann surface of genus one or, equivalently, by an elliptic normal curve E ⊆ CPⁿ⁻¹. The symplectic leaves are described in terms of higher secant varieties to E.