Document Type
Article
Publication Date
2005
Publication Title
Transactions of the American Mathematical Society
Abstract
Consider an -dimensional projective toric variety defined by a convex lattice polytope . David Cox introduced the toric residue map given by a collection of divisors on . In the case when the are -invariant divisors whose sum is , the toric residue map is the multiplication by an integer number. We show that this number is the degree of a certain map from the boundary of the polytope to the boundary of a simplex. This degree can be computed combinatorially. We also study radical monomial ideals of the homogeneous coordinate ring of . We give a necessary and sufficient condition for a homogeneous polynomial of semiample degree to belong to in terms of geometry of toric varieties and combinatorics of fans. Both results have applications to the problem of constructing an element of residue one for semiample degrees.
Repository Citation
Soprunov, Ivan, "Toric Residue and Combinatorial Degree" (2005). Mathematics and Statistics Faculty Publications. 275.
https://engagedscholarship.csuohio.edu/scimath_facpub/275
DOI
10.1090/S0002-9947-04-03770-5
Version
Postprint
Publisher's Statement
First published in Trans. Amer. Math. Soc. 357:5 (2005), published by the American Mathematical Society. © 2005 American Mathematical Society.
Volume
357
Issue
5
