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Reduction numbers, Rees algebras and Pfaffian ideals. (English) Zbl 0838.13003
This paper is concerned with practical methods of testing the Cohen-Macaulay property of the Rees algebra or the form ring of an ideal \(I\) in a Cohen-Macaulay (or Gorenstein) local ring \(R\). In theorem 2.2 the authors establish bounds on the reduction numbers of certain ideals \(I \subset R\) (e.g. unmixed, generically a complete intersection of analytic deviation 1) with Cohen-Macaulay form ring – via a presentation matrix of \(I\). The main application of theorem 2.2 and its corollaries is to a family of 5-generated height 3 Gorenstein ideals of a Gorenstein (in particular of a regular) local ring \(R\) in theorem 3.1. An analogue of this theorem is given in theorem 2.11 for 4-generated height 2 Cohen-Macaulay ideals \(I\) of a Cohen-Macaulay local ring \(R\).
Reviewer: M.Herrmann (Köln)

13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
Full Text: DOI
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