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arXiv · 2101.04845

An algebraic construction of sum-integral interpolators

Benjamin Fischer·James Pommersheim
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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.

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Benjamin Fischer, James Pommersheim. 2021-01-13. An algebraic construction of sum-integral interpolators. https://arxiv.org/abs/2101.04845

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