Algebraic Independence in SL(3,C) Character Varieties of Free Groups

TL;DR

This paper identifies maximal algebraically independent coordinate subsets in the SL(3,C) character variety of free groups, providing local parameters for the moduli space.

Contribution

It describes maximal algebraically independent subsets of coordinate functions that locally parametrize the SL(3,C) character variety of free groups.

Findings

Identified maximal algebraically independent coordinate subsets

Provided local parametrizations of the moduli space

Enhanced understanding of the structure of SL(3,C) character varieties

Abstract

Let X be the moduli space of SL(3,C) representations of a free group of rank r. In this paper we describe maximal algebraically independent subsets of certain minimal sets of coordinate functions on X. These subsets locally parametrize the moduli space.