The moment map and line bundles over presymplectic toric manifolds

Abstract

We apply symplectic methods in studying smooth toric varieties with a closed, invariant 2-form that may have degeneracies. Consider the push-forward of Liouville measure by the moment map. We show that it is a "twisted polytope" in t* which is determined by the winding numbers of a map S n ~ -> t* around points in t* . The index of an equivariant, holomorphic line-bundle with curvature is a virtual Trepresentation which can easily be read from this "twisted polytope".