Transactions of the American Mathematical Society

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



The Castelnuovo regularity of the Rees algebra
and the associated graded ring

Author: Ngô Viêt Trung
Journal: Trans. Amer. Math. Soc. 350 (1998), 2813-2832
MSC (1991): Primary 13A30; Secondary 13D45
MathSciNet review: 1473456
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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

Ngô Viêt Trung
Affiliation: Institute of Mathematics, Box 631, Bò Hô, Hanoi, Vietnam

Keywords: Rees algebra, associated graded ring, Castelnuovo regularity, relation type, reduction number, $d$-sequence, filter-regular sequence
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
Article copyright: © Copyright 1998 American Mathematical Society