RESIDUES IN TORIC VARIETIES

We study residues on a complete toric variety X, which are defined in terms of the homogeneous coordinate ring of X. We first prove a global transformation law for toric residues. When the fan of the toric vari ety has a simplicial cone of maximal dimension, we can produce an elem ent with toric residue equal to 1. We also show that in certain situat ions, the toric residue is an isomorphism on an appropriate graded pie ce of the quotient ring. When X is simplicial, we prove that the toric residue is a sum of local residues. In the case of equal degrees, we also show how to represent X as a quotient (Y\{0})/C such that the to ric residue becomes the local residue at 0 in Y.