Poisson 2014 - Toric Log symplectic manifolds (Gualtieri)

Tuesday, August 5, 2014

Marco Gualtieri (University of Toronto)
Toric Log symplectic manifolds

A log symplectic manifold with toric symmetry cannot admit a momentum map in the usual sense, as this would be singular along the degeneracy locus of the Poisson structure. We show that for a large class of log symplectic manifolds, a 'tropical moment map' may be dened, taking values in a manifold which is glued together from partial compactications of ane space. We provide explicit constructions and classications of these toric log symplectic manifolds, and indicate the relation with tropical geometry.