Gorenstein liaison and ACM sheaves

By Marta Casanellas, E. Drozd, Robin Hartshorne. 2003

68 citations recorded by the source corpus.

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 ℙ n 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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d2956bdd1b66415a62fdda751946964bf3b6876d

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In Algebra and Number Theory

1. R. Mir'o-Roig
2. J. Pons-Llopis
3. L. Costa

In Geometry and Topology

1. R. Mir'o-Roig
2. J. Pons-Llopis
3. L. Costa

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