Cohen-Macaulay fiber cones and defining ideal of Rees algebras of modules

Abstract

Generic Bourbaki ideals were introduced by Simis, Ulrich and Vasconcelos to study the Cohen-Macaulay property of Rees algebras of modules. In this article we prove that the same technique can sometimes be used to investigate the Cohen-Macaulay property of fiber cones of modules and to study the defining ideal of Rees algebras. This is possible as long as the Rees algebra of a given module $E$ is a deformation of the Rees algebra of a generic Bourbaki ideal $I$ of $E$. Our main technical result provides a deformation condition that in fact extends the applicability of generic Bourbaki ideals to situations not covered by previous work.

20 pages. In this versions we added details to some proofs and fixed typos appearing in the previous versions. Some of the content of Section 5 had been previously included in version 1 of arXiv:1811.08402, but does not appear in any of the updated versions of arXiv:1811.08402