Non-exactness of toric Poisson structures

Abstract

We prove that a Poisson structure on a projective toric variety which is invariant by the torus action and whose symplectic leaves are the torus orbits is not exact. This is deduced from a geometric criterion for non-exactness of Poisson structures with a finite number of symplectic leaves.

References in corpus (2)

• Desingularizing $b^m$-symplectic structures
• The geometry of E-manifolds