On the Cohen-Macaulay property of the Rees algebra of the module of differentials

Abstract

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.

On Rees algebras of ideals and modules over hypersurface rings

“…However, much progress has been made in recent years (see e.g. [29,6,7,27,22,10]). Many of the difficulties have been greatly reduced with the innovation of generic Bourbaki ideals.…”