For hyperplane arrangements satisfying a mild condition, the top-dimensional part and radical of the Jacobian ideal are arithmetically Cohen-Macaulay, and liaison constructions produce arrangements whose singular curves have prescribed Hartshorne-Rao modules.
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Schemes supported on the singular locus of a hyperplane arrangement in $\mathbb P^n$
For hyperplane arrangements satisfying a mild condition, the top-dimensional part and radical of the Jacobian ideal are arithmetically Cohen-Macaulay, and liaison constructions produce arrangements whose singular curves have prescribed Hartshorne-Rao modules.