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Rees algebras of non-singular equimultiple prime ideals*

Published online by Cambridge University Press:  22 January 2016

M. Herrman, ,
J. Ribbe  and
N.V. Trung
M. Herrman,
Affiliation:
Mathematisches Institut der Universität zu Köln, 5000 Köln 41, Germany
J. Ribbe
Affiliation:
Mathematisches Institut der Universität zu Köln, 5000 Köli 41, Germany
N.V. Trung
Affiliation:
Institute of Mathematics, Box 631, Bò Hô, Hanoi Vietnam
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In a recent paper [HI2] the first named author and S. Ikeda have investigated Gorenstein properties under blowing up of height two equimultiple ideals from the arithmetical point of view. The problem is to what extent does the Gorenstein property of the Rees algebra R(a) = of an equimultiple ideal a of a local ring (A, m) describe the structure of A and a. One result is that if A is a generalized Cohen-Mac aulay ring (i.e. a ring of finite local cohomology) with dim (A) ⊇ 4 and if there is an height two equimultiple prime ideal p such that R(p) is Gorenstein, then A is Gorenstein and p is generated by a regular sequence (see [HI2], Theorem 2.6). That has led to the question whether this result is still valid for dim (∧) = 3. ∧ partial answer was given in [HI2], Proposition 2.10, where “equimultiplicity” was replaced by the stronger condition “p/p2 is flat over A/p”

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 124 , December 1991 , pp. 1 - 12
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1991

Footnotes

*

We thank the referee for his detailed suggestions and improvements.

References

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