The tropical momentum map: a classification of toric log symplectic manifolds

Abstract

We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization of affine space called a log affine manifold. Using this momentum map, we obtain a complete classification of such manifolds in terms of decorated log affine polytopes, hence extending the classification of symplectic toric manifolds achieved by Atiyah, Guillemin-Sternberg, Kostant, and Delzant.

41 pages, updated section 3

References in corpus (1)

• Elliptic singularities on log symplectic manifolds and Feigin--Odesskii Poisson brackets

Cited by in corpus (4)

• Examples of integrable and non-integrable systems on singular symplectic manifolds
• Cotangent models for integrable systems
• Non-commutative integrable systems on $b$-symplectic manifolds
• Locally standard torus actions and h'-vectors of simplicial posets