LECTURE 2 RESIDUE FORMULAE FOR VOLUMES AND NUMBER OF INTEGRAL POINTS IN CONVEX RATIONAL POLYTOPES

Michèle Vergne
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Michèle Vergne: Centre de Mathematiques, Ecole Polytechnique, F-91128 Palaiseau Cedex, France

Chapter 14 in European Women in Mathematics, 2003, pp 245-285 from World Scientific Publishing Co. Pte. Ltd.

Abstract: AbstractWe first discuss here some classical results on the number of points with integral coordinates in convex rational polytopes P ⊂ Rn starting with Ehrhart's theorem. Then, following Baldoni-Vergne and Szenes-Vergne, we present some recent results giving number of points with integral coordinates in P in terms of multidimensional residues. In particular, this allows to recover relations established by Khovanskii-Pukhlikov, Cappell-Shaneson and Brion-Vergne between volumes and number of points with integral coordinates in families of polytopes with parallel facets.

Keywords: Mathematical Finance; Geometry; Cohomology (search for similar items in EconPapers)
Date: 2003
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