Helly dimension of algebraic groups

Abstract

It is shown that for a linear algebraic group G over a field of characteristic zero, there is a natural number \kappa(G) such that if a system of Zariski closed cosets in G has empty intersection, then there is a subsystem consisting of at most \kappa(G) cosets with empty intersection. This is applied to the study of algebraic group actions on product varieties.Comment: 18 page