On Hodge Polynomials of Singular Character Varieties

Abstract

Let XΓG:=Hom(Γ,G)∕∕G be the G-character variety of Γ, where G is a complex reductive group and Γ a finitely presented group. We introduce new techniques for computing Hodge-Deligne and Serre polynomials of XΓG, and present some applications, focusing on the cases when Γ is a free or free abelian group. Detailed constructions and proofs of the main results will appear elsewhere.