Duality and the equations of Rees rings and tangent algebras

Matthew Weaver

Mathematische Nachrichten, 2025, vol. 298, issue 10, 3394-3416

Abstract: Let E$E$ be a module of projective dimension 1 over a Noetherian ring R$R$ and consider its Rees algebra R(E)$\mathcal {R}(E)$. We study this ring as a quotient of the symmetric algebra S(E)$\mathcal {S}(E)$ and consider the ideal A$\mathcal {A}$ defining this quotient. In the case that S(E)$\mathcal {S}(E)$ is a complete intersection ring, we employ a duality between A$\mathcal {A}$ and S(E)$\mathcal {S}(E)$ in order to study the Rees ring R(E)$\mathcal {R}(E)$ in multiple settings. In particular, when R$R$ is a complete intersection ring defined by quadrics, we consider its module of Kähler differentials ΩR/k$\Omega _{R/k}$ and its associated tangent algebras.

Date: 2025
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