Poisson $C^\infty$-schemes
Symplectic Geometry
2025-09-24 v2 Mathematical Physics
Algebraic Geometry
math.MP
Abstract
We introduce Poisson -rings and Poisson local -ringed spaces. We show that the spectrum of a Poisson -ring is an affine Poisson -scheme. We then discuss applications that include singular symplectic and Poisson reductions, singular quasi-Poisson reduction, coisotropic reduction and Poisson-Dirac subschemes.
Keywords
Cite
@article{arxiv.2507.18621,
title = {Poisson $C^\infty$-schemes},
author = {Eugene Lerman},
journal= {arXiv preprint arXiv:2507.18621},
year = {2025}
}
Comments
24 pages, v2: reorganization and some typos corrected, comments welcome. arXiv admin note: text overlap with arXiv:2503.19064