  We characterize the image of the period map for cubic fourfolds with at worst
simple singularities as the complement of an arrangement of hyperplanes in the
period space. It follows then that the GIT compactification of the moduli space
of cubic fourfolds is isomorphic to the Looijenga's compactification associated
to this arrangement. This work builds on and is a natural continuation of our
previous paper on the GIT compactification of the moduli space of cubic
fourfolds.
