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.
Categories: math.AG math.AC