Non-standard components of the character variety for a family of   Montesinos knots
  We show that there are Montesinos knots with $n+1\geq 4$ tangles whose character varieties contain arbitrarily many irreducible components of dimension $d$ for any $1\le d\le n-2$. Moreover, these irreducible components can be chosen so that the trace of the meridian is non-constant. 
Luisa Paoluzzi and Joan Porti
math.GT