Residual intersections and modules with Cohen-Macaulay Rees algebra
Let \(R\) be a Gorenstein local ring and \(E\) a finite, torsion-free \(R\)-module with a rank. In the paper under review the author provides sufficient conditions for the Rees algebra \(\mathcal{R}(E)\) of \(E\) to be Cohen-Macaulay. As a consequence she obtains sufficient conditions for the Rees algebra of an ideal to be Cohen-Macaulay, and hence recovers a result proved independently by textit{M. Johnson} and \textit{B. Ulrich} [Compos. Math. 103, No. 1, 7--29 (1996; Zbl 0866.13001)], and by \textit{S. Goto} et al. [Am. J. Math. 118, No. 6, 1197--1213 (1996; Zbl 0878.13002)]. In order to prove this result the author first obtains sufficient conditions for \(E\) to be of linear type. This is done by constructing a generic Bourbaki ideal \(I\) of \(E\) and exploiting properties of the residual intersections of \(I\). The author also recovers main results proved by \textit{K.-N. Lin} [Commun. Algebra 44, No. 9, 3673--3682 (2016; Zbl 1360.13014)].
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