Character varieties of mutative 3--manifolds

We describe a birational map between subvarieties in the character varieties of mutative 3-manifolds. By studying the birational map, one can decide in certain circumstances whether a mutation surface is detected by an ideal point of the character variety.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol4/agt-4-9.abs.htm