An algebraic construction of sum-integral interpolators
Algebraic Geometry
2022-05-17 v2 Combinatorics
Abstract
This paper presents an algebraic construction of Euler-Maclaurin formulas for polytopes. The formulas obtained generalize and unite the previous lattice point formulas of Morelli and Pommersheim-Thomas, and the Euler-Maclaurin formulas of Berline-Vergne While the approach of this paper originates in the theory of toric varieties, and recovers previous results about characteristic classes of toric varieties, the present paper is self-contained and does not rely on results from toric geometry. We aim in particular to exhibit in a combinatorial way ingredients such as such Todd classes and cycle-level intersections in Chow rings, that first entered the theory of polytopes from algebraic geometry.
Cite
@article{arxiv.2101.04845,
title = {An algebraic construction of sum-integral interpolators},
author = {Benjamin Fischer and James Pommersheim},
journal= {arXiv preprint arXiv:2101.04845},
year = {2022}
}