1995/06/27 by Eduardo Cattani, David Cox, Cattani, Eduardo +3 · 1 citation
Mathematics · #14M25 #32A25 (Secondary) #32A27 (Primary) #32C30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #alg-geom #math.AG #msc:14M25 #msc:32A25 #msc:32A27 #msc:32C30
paper · pdf · doi:10.48550/arxiv.alg-geom/9506024
35 pages, manuscript dated June 22, 1995, TeX, C Version 3.14t3
arxiv created 1995/06/27 · openalex publication_date 1995/06/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.