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arXiv · 2210.13042

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

Alexandru Chirvasitu·Ryo Kanda·S. Paul Smith
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Abstract

This paper determines the symplectic leaves for a remarkable Poisson structure on $\mathbb{C}\mathbb{P}^{n-1}$ discovered by Feigin and Odesskii, and, independently, by Polishchuk. The Poisson bracket is determined by a holomorphic line bundle of degree $n \ge 3$ on a compact Riemann surface of genus one or, equivalently, by an elliptic normal curve $E\subseteq\mathbb{C}\mathbb{P}^{n-1}$. The symplectic leaves are described in terms of higher secant varieties to $E$.

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Alexandru Chirvasitu, Ryo Kanda, S. Paul Smith. 2022-10-24. The symplectic leaves for the elliptic Poisson bracket on projective space defined by Feigin-Odesskii and Polishchuk. https://arxiv.org/abs/2210.13042

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