  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.
