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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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The Castelnuovo regularity of the Rees algebra and the associated graded ring
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by Ng么 Vi锚t Trung PDF
Trans. Amer. Math. Soc. 350 (1998), 2813-2832 Request permission

Abstract:

It is shown that there is a close relationship between the invariants characterizing the homogeneous vanishing of the local cohomology and the Koszul homology of the Rees algebra and the associated graded ring of an ideal. From this it follows that these graded rings share the same Castelnuovo regularity and the same relation type. The main result of this paper is however a simple characterization of the Castenuovo regularity of these graded rings in terms of any reduction of the ideal. This characterization brings new insights into the theory of $d$-sequences.
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Additional Information
  • Ng么 Vi锚t Trung
  • Affiliation: Institute of Mathematics, Box 631, B貌 H么, Hanoi, Vietnam
  • MR Author ID: 207806
  • Email: nvtrung@thevinh.ac.vn
  • Received by editor(s): June 15, 1996
  • Additional Notes: This work is partially supported by the National Basic Research Program of Vietnam

  • Dedicated: Dedicated to the memory of Professor Hideyuki Matsumura
  • © Copyright 1998 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 350 (1998), 2813-2832
  • MSC (1991): Primary 13A30; Secondary 13D45
  • DOI: https://doi.org/10.1090/S0002-9947-98-02198-9
  • MathSciNet review: 1473456