Deformations of reducible representations of 3-manifold groups into   PSL_2(C)
  Let M a 3-manifold with torus boundary which is a rational homology circle. We study deformations of reducible representations of p_1(M) into PSL_2(C) associated to a simple zero of the twisted Alexander polynomial. We also describe the local structure of the representation and character varieties. 
Michael Heusener, Joan Porti