THE FUNCTOR OF A SMOOTH TORIC VARIETY

Abstract

This paper describes the data needed to specify a map from a scheme to an arbitrary smooth toric variety. The description is in terms of a collection of line bundles and sections on the scheme which satisfy certain compatibility and nondegeneracy conditions. There is also a natural torus action on these collections. As an application, we show how homogeneous polynomials can be used to describe all maps from a pro-jective space (or more generally a toric variety) to a smooth complete toric variety.