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Gustav I. Lehrer
Rational points and Coxeter group actions on the cohomology of toric varieties
(Points rationnels et action d’un groupe de Coxeter sur la cohomologie des variétés toriques)
Annales de l'institut Fourier, 58 no. 2 (2008), p. 671-688, doi: 10.5802/aif.2364
Article PDF | Reviews MR 2410386 | Zbl 1148.14026
Class. Math.: 14M25, 14F40, 14G05, 20G40, 14L30
Keywords: Toric varieties, cohomology, Hodge theory, rational points

Résumé - Abstract

We derive a simple formula for the action of a finite crystallographic Coxeter group on the cohomology of its associated complex toric variety, using the method of counting rational points over finite fields, and the Hodge structure of the cohomology. Various applications are given, including the determination of the graded multiplicity of the reflection representation.

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