Smooth Character Varieties for Torus Knot Groups
  Semisimple representations of the free product Z_p*Z_q determine \theta-semistable representations of a specific quiver Q_pq. The dimension vectors of \theta-stable representations of this quiver were classified by Le Bruyn and Adriaenssens. In this paper we classify the moduli spaces M_\alpha^ss(Q_pq,\theta) which are smooth projective varieties. 
Jan Adriaenssens, Raf Bocklandt and Geert Van de Weyer