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arXiv · 2306.14719

Bosonization of Feigin-Odesskii Poisson varieties

Zheng Hua·Alexander Polishchuk
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Abstract

The derived moduli stack of complexes of vector bundles on a Gorenstein Calabi-Yau curve admits a 0-shifted Poisson structure. Feigin-Odesskii Poisson varieties are examples of such moduli spaces over complex elliptic curves. Using moduli stack of chains we construct an auxiliary Poisson varieties with a Poisson morphism from it to a Feigin-Odesskii variety. We call it the \emph{bosonization} of Feigin-Odesskii variety. As an application, we show that the Feigin-Odesskii Poisson brackets on projective spaces (associated with stable bundles of arbitrary rank on elliptic curves) admit no infinitesimal symmetries.

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Zheng Hua, Alexander Polishchuk. 2023-06-26. Bosonization of Feigin-Odesskii Poisson varieties. https://arxiv.org/abs/2306.14719

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