English

Poisson $C^\infty$-schemes

Symplectic Geometry 2025-09-24 v2 Mathematical Physics Algebraic Geometry math.MP

Abstract

We introduce Poisson CC^\infty-rings and Poisson local CC^\infty-ringed spaces. We show that the spectrum of a Poisson CC^\infty-ring is an affine Poisson CC^\infty-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

R2 v1 2026-07-01T04:17:29.546Z