THE MOMENT MAP AND LINE BUNDLES OVER PRESYMPLECTIC TORIC MANIFOLDS

We apply symplectic methods in studying smooth toric varieties with a closed, invariant 2-form omega 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-1) --> t* around points in t*. The index of an equivariant, holomorphic line-bundle with curvature omega is a virtual T-representation which can easily be read from this 'twisted polytope''.