I will present a joint work with Joan Porti (UAB) in which the SL₂(C)-character varieties of a family of Montesinos knots are studied and the existence of high-dimensional irreducible components, different from the Teichmüller one, is established.

 

The interest of these varieties stems from the fact that they provide toy-examples of possible "ramification" phenomena that can occur when considering character varieties over algebraically closed fields of positive charcateristic, instead of over the field C of complex numbers. I shall briefly discuss why one may want to understand this type of phenomena and, if time permits, hint to other examples where a different "ramification" behaviour is observed (this is work in progress, again in collaboration with J. Porti). 

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