English

Bosonization of Feigin-Odesskii Poisson varieties

Algebraic Geometry 2023-06-27 v1 Quantum Algebra Symplectic 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.

Keywords

Cite

@article{arxiv.2306.14719,
  title  = {Bosonization of Feigin-Odesskii Poisson varieties},
  author = {Zheng Hua and Alexander Polishchuk},
  journal= {arXiv preprint arXiv:2306.14719},
  year   = {2023}
}