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Characterization of some projective subschemes by locally free resolutions

2002/12/16 by Uwe Nagel, Nagel, Uwe
Mathematics · #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG

paper · pdf · doi:10.48550/arxiv.math/0212217

Contemp. Math. (to appear)

arxiv created 2002/12/16 · arxiv updated 2009/11/30

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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