Hodge polynomials of SL (2,C)-character varieties for curves of small genus

Abstract

We compute the E-polynomials of the moduli spaces of representations of the fundamental group of a complex curve into for the case of small genus and allowing the holonomy around a fixed point to be any matrix of that is diagonalisable, or of either of the two Jordan types. For this, we introduce a new geometric technique, based on stratifying the space of representations, and on the analysis of the behaviour of the E-polynomial under fibrations