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

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dc.creatorLawton, Sean
dc.date2007-09-27
dc.date2008-07-03
dc.date.accessioned2026-07-07T12:11:30Z
dc.date.available2026-07-07T12:11:30Z
dc.descriptionLet 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).
dc.description49 pages, 9 tables; this version (accepted for publication in Journal of Algebra) has some minor corrections, substantial reorganization, and some added references
dc.identifierhttps://arxiv.org/abs/0709.4403
dc.identifierhttp://arxiv.org/abs/0709.4403
dc.identifierJournal of Algebra, Volume 320, Issue 10, 15 November 2008, Pages 3773-3810
dc.identifierdoi:10.1016/j.jalgebra.2008.06.031
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210236
dc.subjectAlgebraic Geometry
dc.subjectCommutative Algebra
dc.subject16R10, 16R30
dc.titleMinimal Affine Coordinates for SL(3,C) Character Varieties of Free Groups
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