Minimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups

Abstract

Let X be the moduli of SL(3,C) representations of a rank r free group. In this paper we determine minimal generators of the coordinate ring of X. This at once gives explicit global coordinates for the moduli and determines the dimension of the moduli's minimal affine embedding. Along the way, we utilize results concerning the moduli of r-tuples of matrices in gl(3,C). Consequently, we also state general invariant theoretic correspondences between the coordinate rings of the moduli of r-tuples of elements in gl(n,C), sl(n,C), and SL(n,C).

arXiv comment49 pages, 9 tables; this version (accepted for publication in Journal of Algebra) has some minor corrections, substantial reorganization, and some added references

References in corpus (2)

• Generators, Relations and Symmetries in Pairs of 3x3 Unimodular Matrices
• Defining relations of invariants of two 3 \times 3 matrices

Cited by in corpus (11)

• Geometry of the SL(3,C)-character variety of torus knots
• E-polynomial of the SL(3,C)-character variety of free groups
• Rank 1 character varieties of finitely presented groups
• Algebraic Independence in SL(3,C) Character Varieties of Free Groups
• Varieties of Characters
• Ergodicity of Mapping Class Group Actions on SU(2)-character varieties
• Invariants of pairs in SL(4,C) and SU(3,1)
• Obtaining the One-Holed Torus from Pants: Duality in an SL(3,C)-Character Variety
• Motive of the $S{L}_4$-character variety of torus knots
• Special elliptic isometries, relative SU(2,1)-character varieties, and bendings
• Representation varieties of twisted Hopf links