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

2020/07/30 by Costantini, Alessandra, Dang, Tan
#13-00 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.15772

Abstract

Let R be an algebra essentially of finite type over a field k and let Ω_k(R) be its module of Kähler differentials over k. If R is a homogeneous complete intersection and char(k)=0, we prove that Ω_k(R) is of linear type whenever its Rees algebra is Cohen-Macaulay and locally at every homogeneous prime \mathfrakp the embedding dimension of R_\mathfrakp is at most twice its dimension.

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