THE FUNCTOR OF A TORIC VARIETY WITH ENOUGH INVARIANT EFFECTIVE CARTIER DIVISORS

The homogeneous coordinate ring of a toric variety was first introduce d by Cox. In this paper, we study that of a toric variety with enough invariant effective Cartier divisors in detail. Here a toric variety i s said to have enough invariant effective Cal tier divisors if, for ea ch nonempty affine open subset stable under the action of the torus, t here exists an effective Cartier divisor whose support equals its comp lement. Both quasi-projective toric varieties and simplicial toric var ieties have enough invariant effective Cartier divisors. In terms of t he homogeneous coordinate ring, we describe the data needed to specify a morphism from a scheme to such a toric variety. As a consequence, w e generalize a result of Cox, one of Oda and Sankaran, and one of Gues t concerning data on morphisms.