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 κ(G) such that if a system of Zariski closed cosets in G has empty intersection, then there is a subsystem consisting of at most κ(G) cosets with empty intersection. This is applied to the study of algebraic group actions on product varieties.

18 pages

References in corpus (2)

• Separating algebras and finite reflection groups
• The Cohen-Macaulay property of separating invariants of finite groups

Cited by in corpus (5)

• Separating invariants for multisymmetric polynomials
• Degree bounds for fields of rational invariants of $\mathbb{Z}/p\mathbb{Z}$ and other finite groups
• The Noether number of the non-abelian group of order 3p
• Separating invariants for arbitrary linear actions of the additive group
• Degree bound for separating invariants of abelian groups