  We discuss the vacuum structure of type IIA/B Calabi-Yau string
compactifications to four dimensions in the presence of n-form H-fluxes. These
will lift the vacuum degeneracy in the Calabi-Yau moduli space, and for generic
points in the moduli space, N=2 supersymmetry will be broken. However, for
certain `aligned' choices of the H-flux vector, supersymmetric ground states
are possible at the degeneration points of the Calabi-Yau geometry. We will
investigate in detail the H-flux induced superpotential and the corresponding
scalar potential at several degeneration points, such as the Calabi-Yau large
volume limit, the conifold loci, the Seiberg-Witten points, the strong coupling
point and the conformal points. Some emphasis is given to the question whether
partial supersymmetry breaking can be realized at those points. We also relate
the H-flux induced superpotential to the formalism of gauged N=2 supergravity.
Finally we point out the analogies between the Calabi-Yau vacuum structure due
to H-fluxes and the attractor formalism of N=2 black holes.
