THE FUNCTOR OF A SMOOTH TORIC VARIETY

This paper describes that date needed to specify a map from a scheme t o an arbitrary smooth toric variety. The description is in terms of a collection of line bundles and sections on the scheme which satisfy ce rtain compatibility and nondegeneracy conditions. There is also a natu ral torus action on these collections. As an application, we show how homogeneous polynomials can be used to describe all maps from a projec tive space (or more generally a toric variety) to a smooth complete to ric variety.