Elliptic bihamiltonian structures from relative shifted Poisson structures
Algebraic Geometry
2023-11-06 v2 Quantum Algebra
Symplectic Geometry
Abstract
In this paper, generalizing the construction of \cite{HP1}, 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 \cite{OW}.
Cite
@article{arxiv.2007.12351,
title = {Elliptic bihamiltonian structures from relative shifted Poisson structures},
author = {Zheng Hua and Alexander Polishchuk},
journal= {arXiv preprint arXiv:2007.12351},
year = {2023}
}
Comments
This is an updated version to appear on Journal of Topology