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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Arithmetically Buchsbaum divisors
on varieties of minimal degree

Author: Uwe Nagel
Journal: Trans. Amer. Math. Soc. 351 (1999), 4381-4409
MSC (1991): Primary 14M05; Secondary 13H10
Published electronically: April 20, 1999
MathSciNet review: 1615938
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Abstract: In this paper we consider integral arithmetically Buchsbaum subschemes of projective space. First we show that arithmetical Buchsbaum varieties of sufficiently large degree have maximal Castelnuovo-Mumford regularity if and only if they are divisors on a variety of minimal degree. Second we determine all varieties of minimal degree and their divisor classes which contain an integral arithmetically Buchsbaum subscheme. Third we investigate these varieties. In particular, we compute their Hilbert function, cohomology modules and (often) their graded Betti numbers and obtain an existence result for smooth arithmetically Buchsbaum varieties.

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Additional Information

Uwe Nagel
Affiliation: Fachbereich Mathematik und Informatik, Universität-Gesamthochschule Paderborn, D–33095 Paderborn, Germany

Keywords: Minimal generator, local cohomology, Castelnuovo-Mumford regularity, arithmetically Buchsbaum scheme, rational normal scroll
Received by editor(s): August 27, 1997
Published electronically: April 20, 1999
Additional Notes: The material of this paper is part of the author’s Habilitationsschrift \cite{hab}.
Article copyright: © Copyright 1999 American Mathematical Society