Smooth Character Varieties for Torus Knot Groups

2000/12/15 by Jan Adriaenssens, Raf Bocklandt, Adriaenssens, Jan +3
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT

paper · pdf · doi:10.48550/arxiv.math/0012120

12 pages

arxiv created 2000/12/15 · openalex publication_date 2000/12/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Semisimple representations of the free product Z_p*Z_q determine θ-semistable representations of a specific quiver Q_pq. The dimension vectors of θ-stable representations of this quiver were classified by Le Bruyn and Adriaenssens. In this paper we classify the moduli spaces M_α^ss(Q_pq,θ) which are smooth projective varieties.

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