Let $E$ be a module of projective dimension one over a Noetherian ring $R$ and consider its Rees algebra $\mathcal{ R}(E)$. We study this ring as a quotient of the symmetric algebra $\mathcal{ S}(E)$ and consider the ideal $\mathcal{ A}$ defining this quotient. In the case that $\mathcal{ S}(E)$ is a complete intersection ring, we employ a duality between $\mathcal{ A}$ and $\mathcal{ S}(E)$ in order to study the Rees ring $\mathcal{ R}(E)$ in multiple settings. In particular, when $R$ is a complete intersection ring defined by quadrics, we consider its module of K\"ahler differentials $\Omega_{ R/k}$ and its associated tangent algebras.
Categories: math.AC