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Gorenstein Liaison and ACM Sheaves

Marta Casanellas·Elena Drozd·Robin Hartshorne
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Abstract

We study Gorenstein liaison of codimension two subschemes of an arithmetically Gorenstein scheme X. Our main result is a criterion for two such subschemes to be in the same Gorenstein liaison class, in terms of the category of ACM sheaves on X. As a consequence we obtain a criterion for X to have the property that every codimension 2 arithmetically Cohen-Macaulay subscheme is in the Gorenstein liaison class of a complete intersection. Using these tools we prove that every arithmetically Gorenstein subscheme of $\mathbb{P}^n$ is in the Gorenstein liaison class of a complete intesection and we are able to characterize the Gorenstein liaison classes of curves on a nonsingular quadric threefold in $\mathbb{P}^4$.

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Marta Casanellas, Elena Drozd, Robin Hartshorne. 2003-07-29. Gorenstein Liaison and ACM Sheaves. https://arxiv.org/abs/math/0307378

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