ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14, 13 Nagel, Uwe, Universität-Gesamthochschule Paderborn, Germany Characterization of projective subschemes by locally free resolutions A locally free resolution of a subscheme is an exact sequence consisting of locally free sheaves (apart from the ideal sheaf of the subscheme) which has uniqueness properties like a free resolution. Such resolutions do exist. We use them in order to characterize certain locally Cohen-Macaulay subschemes. Firstly, we achieve this for arithmetically Buchsbaum subschemes. This leads to the notion of an Ω-resolution and extends the main result of Chang in [1]. Secondly, we characterize quasi-Buchsbaum subschemes by means of weak Ω-resolutions. Finally, we describe the weak Ω-resolutions which belong to arithmetically Buchsbaum surfaces in ℙ^{4}.

Reference: [1] M. Chang, Characterization of arithmetically Buchsbaum subschemes of codimension 2 in ℙ^{n}, J. Differential Geom. 31 (1990), 323–341.