Residues in Toric Varieties

Details Residues in Toric Varieties Residues in Toric Varieties

1995-06-27

arxiv.org/abs/alg-geom/9506024v1

Mathematics

Algebraic Geometry

35 pages, manuscript dated June 22, 1995, TeX, C Version 3.14t3

Scientific paper

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.

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