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

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**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.## References

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## Additional Information

**Ngô Viêt Trung**- Affiliation: Institute of Mathematics, Box 631, Bò Hô, 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
- © 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

Dedicated: Dedicated to the memory of Professor Hideyuki Matsumura