Residues in Toric Varieties

Cattani, Eduardo; Cox, David; Dickenstein, Alicia

Residues in Toric Varieties

Authors

Cattani, Eduardo

Cox, David

Dickenstein, Alicia

Description

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 variety has a simplicial cone of maximal dimension, we can produce an element with toric residue equal to 1. We also show that in certain situations, the toric residue is an isomorphism on an appropriate graded piece 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 toric residue becomes the local residue at 0 in Y.
35 pages, manuscript dated June 22, 1995, TeX, C Version 3.14t3