Compatible Feigin-Odesskii Poisson brackets

Nikita Markarian; Alexander Polishchuk

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arXiv · 2207.07770

Compatible Feigin-Odesskii Poisson brackets

Nikita Markarian·Alexander Polishchuk

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Abstract

We prove that several Feigin-Odesskii Poisson brackets associated with normal elliptic curves in ${\mathbb P}^n$ are compatible if and only if they are contained in a scroll or in a Veronese surface in ${\mathbb P}^5$ (with an exception of one case when $n=3$). In the case $n=3$ we determine the quartic corresponding to the Schouten bracket of two (non-compatible) Poisson brackets associated with normal elliptic curves $E_1$ and $E_2$.

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Nikita Markarian, Alexander Polishchuk. 2022-07-30. Compatible Feigin-Odesskii Poisson brackets. https://arxiv.org/abs/2207.07770

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