Glasgow Mathematical Journal

Table of Contents - 2011 - Volume 53, Issue 01  

Research Article

ON THE NUMBER OF POINTS OVER FINITE FIELDS ON VARIETIES RELATED TO CLUSTER ALGEBRAS

F. CHAPOTONa1

a1 Institut Camille Jordan, Université Claude Bernard Lyon 1, Bâtiment Braconnier, 21 Avenue Claude Bernard, F-69622 Villeurbanne Cedex, France e-mail: chapoton@math.univ-lyon1.fr

Abstract

We start here the study of some algebraic varieties related to cluster algebras. These varieties are defined as the fibres of the projection map from the cluster variety to the affine space of coefficients. We compute the number of points over finite fields on these varieties, for all simply laced Dynkin diagrams. We also compute the cohomology with compact support in some cases.

(Received April 21 2010)

(Accepted August 28 2010)

2010 Mathematics Subject Classification

  • 14R;
  • 16G20