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Characterization of some projective subschemes by locally free resolutions

Uwe Nagel
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Abstract

A locally free resolution of a subscheme is by definition an exact sequence consisting of locally free sheaves (except the ideal sheaf) which has uniqueness properties like a free resolution. The purpose of this paper is to characterize certain locally Cohen-Macaulay subschemes by means of locally free resolutions. First we achieve this for arithmetically Buchsbaum subschemes. This leads to the notion of an $Ω$-resolution and extends a result of Chang. Second we characterize quasi-Buchsbaum subschemes by means of weak $Ω$-resolutions. Finally, we describe the weak $Ω$-resolutions which belong to arithmetically Buchsbaum surfaces of codimension two. Various applications of our results are given.

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Uwe Nagel. 2002-12-16. Characterization of some projective subschemes by locally free resolutions. https://arxiv.org/abs/math/0212217

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