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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Arithmetically Buchsbaum divisors on varieties of minimal degree
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by Uwe Nagel PDF
Trans. Amer. Math. Soc. 351 (1999), 4381-4409 Request permission

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
  • MR Author ID: 248652
  • Email: uwen@uni-paderborn.de
  • 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 [On arithmetically Buchsbaum subschemes and liaison, Habilitationsschrift, Paderborn 1996].
  • © Copyright 1999 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 351 (1999), 4381-4409
  • MSC (1991): Primary 14M05; Secondary 13H10
  • DOI: https://doi.org/10.1090/S0002-9947-99-02357-0
  • MathSciNet review: 1615938