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Let $R$ be an algebra essentially of finite type over a field $k$ and let$\Omega_k(R)$ be its module of K\"ahler differentials over $k$. If $R$ is ahomogeneous complete intersection and $\mathrm{char}(k)=0$, we prove that$\Omega_k(R)$ is of linear type whenever its Rees algebra is Cohen-Macaulay andlocally at every homogeneous prime $\mathfrak{p}$ the embedding dimension of$R_{\mathfrak{p}}$ is at most twice its dimension.

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