Residual intersections and modules with Cohen-Macaulay Rees algebra

Abstract

In this paper, we consider a finite, torsion-free module $E$ over a Gorenstein local ring. We provide sufficient conditions for $E$ to be of linear type and for the Rees algebra $\mathcal{R}(E)$ of $E$ to be Cohen-Macaulay. Our results are obtained by constructing a generic Bourbaki $I$ ideal of $E$ and exploiting properties of the residual intersections of $I$.

20 pages. Previously uploaded under the title "On the Cohen-Macaulayness and defining ideal of Rees algebras of modules". Section 3 from the first version has been expanded and now occupies Sections 3 and 4. Content of former Section 4 now appears in arXiv:2011.08453