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Rees algebras of ideals having small analytic deviation. (English) Zbl 0813.13009
Summary: 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.

MSC:
13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
13C14 Cohen-Macaulay modules
13C05 Structure, classification theorems for modules and ideals in commutative rings
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
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