  We study the geometry of the morphism between moduli spaces of hypersurfaces
in $\mathbb P^{n-1}$ that sends a smooth hypersurface of degree $d+1$ to its
associated hypersurface of degree $n(d-1)$. As a result, we obtain a
compactification of the moduli space of smooth hypersurfaces such that the
induced rational map from the standard GIT compactification often contracts the
discriminant divisor.
