Poisson C^∞-schemes

2025/07/24 by Eugene Lerman, Lerman, Eugene
Engineering · Mathematics · Computer Science · #Advanced Numerical Methods in Computational Mathematics #Differential Equations and Numerical Methods #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2507.18621

Abstract

We introduce Poisson C^∞-rings and Poisson local C^∞-ringed spaces. We show that the spectrum of a Poisson C^∞-ring is an affine Poisson C^∞-scheme. We then discuss applications that include singular symplectic and Poisson reductions, singular quasi-Poisson reduction, coisotropic reduction and Poisson-Dirac subschemes.

Citations

• Normalisation of a Poisson algebra is Poisson
• Quasi-Poisson Manifolds
• Quasi-Poisson Manifolds
• Proper group actions and symplectic stratified spaces

Related

• Poisson catenarity in Poisson nilpotent algebras
• Extensions of Poisson Structures on Singular Hypersurfaces
• Poisson resolutions
• On the splitting of infinitesimal Poisson automorphisms around symplectic leaves
• Nonabelian elliptic Poisson structures on projective spaces