Bosonization of Feigin-Odesskii Poisson varieties

2023/06/26 by Zheng Hua, Hua, Zheng, Alexander Polishchuk +1
Mathematics · Pharmacology, Toxicology and Pharmaceutics · #14F08 #37-XX #53D17 #53D55 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Alkaloids: synthesis and pharmacology #FOS: Mathematics #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2306.14719

openalex publication_date 2023/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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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• Shifted Poisson structures and moduli spaces of complexes
• Poisson Structures on Moduli Spaces of Higgs Bundles over Stacky Curves
• Feigin-Odesskii brackets associated with Kodaira cycles and positroid varieties
• Elliptic bihamiltonian structures from relative shifted Poisson structures
• The symplectic leaves for the elliptic Poisson bracket on projective space defined by Feigin-Odesskii and Polishchuk