Generic Bourbaki ideals were introduced by Simis, Ulrich and Vasconcelos in [41] 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 in [41].[51] M. Weaver, Rees algebras of ideals and modules over hypersurface and complete intersection rings, Ph.D. thesis, Purdue University, in preparation.

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Let R be an algebra essentially of finite type over a field k and let Ω k pRq be its module of Kähler differentials over k. If R is a homogeneous complete intersection and charpkq " 0, we prove that Ω k pRq is of linear type whenever its Rees algebra is Cohen-Macaulay and locally at every homogeneous prime p the embedding dimension of Rp is at most twice its dimension.

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