Rees algebras of ideals having small analytic deviation

Huckaba, Sam; Huneke, Craig

doi:10.1090/S0002-9947-1993-1123455-7

Rees algebras of ideals having small analytic deviation
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by Sam Huckaba and Craig Huneke

Trans. Amer. Math. Soc. 339 (1993), 373-402

DOI: https://doi.org/10.1090/S0002-9947-1993-1123455-7

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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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