Bosonization of Feigin-Odesskii Poisson varieties

TL;DR

This paper introduces a new bosonization construction for Feigin-Odesskii Poisson varieties using moduli stacks of chains, and demonstrates their symmetry properties.

Contribution

It constructs a bosonization of Feigin-Odesskii varieties via moduli stacks of chains and analyzes their symmetry properties.

Findings

Bosonization provides a new perspective on Feigin-Odesskii varieties.

Feigin-Odesskii Poisson brackets have no infinitesimal symmetries.

The approach links moduli stacks to Poisson geometry.

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.