  This is a r\'esum\'e of an extensive investigation of some examples in which
one obtains the rigid limit of N=2 supergravity by means of an expansion around
singular points in the moduli space of a Calabi-Yau 3-fold. We make extensive
use of the K3 fibration of the Calabi-Yau manifolds which are considered. At
the end the fibration parameter becomes the coordinate of the Riemann surface
whose moduli space realises rigid N=2 supersymmetry.
