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Creators/Authors contains: "Migliore, Juan"

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  1. ; ; ; ; ; ; ; ; (, Communications in Algebra)
    null (Ed.)
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  2. ; ; (, International Mathematics Research Notices)
    Abstract A hyperplane arrangement in $$\mathbb P^n$$ is free if $R/J$ is Cohen–Macaulay (CM), where $$R = k[x_0,\dots ,x_n]$$ and $$J$$ is the Jacobian ideal. We study the CM-ness of two related unmixed ideals: $$ J^{un}$$, the intersection of height two primary components, and $$\sqrt{J}$$, the radical. Under a mild hypothesis, we show these ideals are CM. Suppose the hypothesis fails. For equidimensional curves in $$\mathbb P^3$$, the Hartshorne–Rao module measures the failure of CM-ness and determines the even liaison class of the curve. We show that for any positive integer $$r$$, there is an arrangement for which $$R/J^{un}$$ (resp. $$R/\sqrt{J}$$) fails to be CM in only one degree, and this failure is by $$r$$. We draw consequences for the even liaison class of $$J^{un}$$ or $$\sqrt{J}$$. 
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