Algebraic and geometric solutions of hyperbolicity equations

In this paper, we study the differences between algebraic and geometric solutions of hyperbolicity equations for ideally triangulated 3-manifolds, and their relations with the variety of representations of the fundamental group of such manifolds into PSL ( 2 , C ) . w that the geometric solutions of compatibility equations form an open subset of the algebraic ones, and we prove uniqueness of the geometric solutions of hyperbolic Dehn filling equations. last section we study some examples, doing explicit calculations for three interesting manifolds.