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Freeness is an important property of a hypersurface arrangement, although itspresence is not well understood. A hypersurface arrangement in $\PP^n$ is freeif $S/J$ is Cohen-Macaulay (CM), where $S = K[x_0,\ldots,x_n]$ and $J$ is theJacobian ideal. We study two related unmixed ideals: $J^{top}$, theintersection of height two primary components, and $\sqrt{J}$, the radical.Under mild hypotheses, we show that these ideals are CM. This establishes afull generalization of an earlier result with Schenck from hyperplanearrangements to hypersurface arrangements. If the hypotheses fail for anarrangement in projective $3$-space, the Hartshorne-Rao module measures thefailure of CMness. We establish consequences for the even liaison classes of$J^{top}$ and $\sqrt{J}$.

Jacobian schemes arising from hypersurface arrangements in $\mathbb P^n$