Bosonization of Feigin-Odesskii Poisson varieties
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2023
- DOI:
- 10.48550/arXiv.2306.14719
- arXiv:
- arXiv:2306.14719
- Bibcode:
- 2023arXiv230614719H
- Keywords:
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- Mathematics - Algebraic Geometry;
- Mathematics - Quantum Algebra;
- Mathematics - Symplectic Geometry;
- 14F08;
- 53D17;
- 53D55;
- 37-XX