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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 ℙn is in the Gorenstein liaison class of a complete intersection and we are able to characterize the Gorenstein liaison classes of curves on a nonsingular quadric threefold in ℙ4.
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Published Online: 2005-11-07
Published in Print: 2005-07-26
© Walter de Gruyter
