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Transactions of the American Mathematical Society

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

 

 

Rees algebras of ideals having small analytic deviation


Authors: Sam Huckaba and Craig Huneke
Journal: Trans. Amer. Math. Soc. 339 (1993), 373-402
MSC: Primary 13A30; Secondary 13H10
DOI: https://doi.org/10.1090/S0002-9947-1993-1123455-7
MathSciNet review: 1123455
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Abstract: In this article we identify two large families of ideals of a Cohen-Macaulay (sometimes Gorenstein) local ring whose Rees algebras are Cohen-Macaulay. Our main results imply, for example, that if $ (R,M)$ is a regular local ring and $ P$ is a prime ideal of $ R$ such that $ {P^n}$ is unmixed for all $ n \geq 1$, then the Rees algebra $ R[Pt]$ is Cohen-Macaulay if either $ \dim (R/P) = 2$, or $ \dim (R/P) = 3,R/P$ is Cohen-Macaulay, and $ R/P$ is integrally closed.


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DOI: https://doi.org/10.1090/S0002-9947-1993-1123455-7
Article copyright: © Copyright 1993 American Mathematical Society