2021/01/13 by Benjamin Fischer, Fischer, Benjamin, James Pommersheim +1 · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Commutative Algebra and Its Applications #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2101.04845
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.