Degenerations of ideal hyperbolic triangulations

Let M be the interior of a compact, orientable 3–manifold with non-empty boundary a disjoint union of tori, and T be an ideal triangulation of M . The affine algebraic set D(M ; T ), a subset of which parameterises (incomplete) hyperbolic structures obtained on M using T , is defined and compactified by adding projective classes of transversely measured singular codimension–one foliations of (M ; T ). This leads to a combinatorial and geometric variant of well–known constructions by Culler, Morgan and Shalen concerning the character variety of a 3–manifold. AMS Classification 57M25, 57N10