Barvinok's algorithm and the Todd class of a toric variety
type: Item
instance of: scholarly article
title: Barvinok's algorithm and the Todd class of a toric variety
zbMATH Open document ID: 0910.14027
DOI: 10.1016/S0022-4049(97)00025-X
author: James Pommersheim
published in: Journal of Pure and Applied Algebra
publication date: 1999-04-15T00:00:00Z
review text: Let \(X\) denote the toric variety arising from a complete simplicial fan \(\Delta\). In the present article a canonical expression of the Todd class of \(X\) as a power series in the rays of \(\Delta\) is given. An important property of this power series is that its behaviour under (virtual) subdivisions of \(\Delta\) can be described explicitly. Combining this with Barvinok's algorithm [see \textit{A. I. Barvinok}, Math. Oper. Res. 19, No. 4, 769-779 (1994; Zbl 0821.90085)] the author obtains an effective algorithm to compute the Todd class of \(X\). An application of this method to the problem of counting lattice points of a simple lattice polytope is given.
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 52B20
Mathematics Subject Classification ID: 14F45
Mathematics Subject Classification ID: 55R40
zbMATH DE Number: 1025710
zbMATH Keywords: toric varieties
zbMATH Keywords: Todd class
zbMATH Keywords: counting lattice points
reviewed by: Jürgen Hausen
MaRDI profile type: Publication
cites work: A Polynomial Time Algorithm for Counting Integral Points in Polyhedra When the Dimension is Fixed
cites work: Q5690184
cites work: Genera of algebraic varieties and counting of lattice points
cites work: THE GEOMETRY OF TORIC VARIETIES
cites work: Q3328651
cites work: Introduction to Toric Varieties. (AM-131)
cites work: Values of zeta functions at negative integers, Dedekind sums and toric geometry
cites work: Q3140501
cites work: Pick's theorem and the Todd class of a toric variety
cites work: Q3837472
cites work: Toric varieties, lattice points and Dedekind sums
cites work: Products of Cycles and the Todd Class of a Toric Variety
cites work: Q3840745
description: scientific article; zbMATH DE number 1025710