Elliptic bihamiltonian structures from relative shifted Poisson structures

2020/07/24 by Zheng Hua, Hua, Zheng, Alexander Polishchuk +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2007.12351

openalex publication_date 2020/07/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, generalizing the construction of \citeHP1, we equip the relative moduli stack of complexes over a Calabi-Yau fibration (possibly with singular fibers) with a shifted Poisson structure. Applying this construction to the anticanonical linear systems on surfaces, we get examples of compatible Poisson brackets on projective spaces extending Feigin-Odesskii Poisson brackets. Computing explicitly the corresponding compatible brackets coming from Hirzebruch surfaces, we recover the brackets defined by Odesskii-Wolf in \citeOW.

Citations

• Vector bundles on elliptic curve and Sklyanin algebras

Related

• Shifted Poisson structures and moduli spaces of complexes
• Nonabelian elliptic Poisson structures on projective spaces
• The symplectic leaves for the elliptic Poisson bracket on projective space defined by Feigin-Odesskii and Polishchuk
• Holonomic Poisson geometry of Hilbert schemes
• Bosonization of Feigin-Odesskii Poisson varieties