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

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.

13 pages, v2 contains minor changes

References in corpus (3)

• Generators, Relations and Symmetries in Pairs of 3x3 Unimodular Matrices
• Minimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups
• Invariants of 2 by 2 matrices, irreducible SL(2,C) characters and the Magnus trace map

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• Holomorphic volume forms on representation varieties of surfaces with boundary
• Newton-Okounkov polyhedra for character varieties and configuration spaces
• On SL(3,$\mathbb{C}$)-representations of the Whitehead link group