Rees Algebras and Almost Linearly Presented Ideals

Abstract

Consider a grade 2 perfect ideal $I$ in $R=k[x_1,\cdots ,x_d]$ which is generated by forms of the same degree. Assume that the presentation matrix $\phi$ is almost linear, that is, all but the last column of $\phi$ consist of entries which are linear. For such ideals, we find explicit forms of the defining ideal of the Rees algebra $\mathcal{R}(I)$. We also introduce the notion of iterated Jacobian duals.

Cited by in corpus (4)

• The equations defining blowup algebras of height three Gorenstein ideals
• Equations of Rees algebras of ideals in two variables
• Rees algebra of maximal order Pfaffians and its diagonal subalgebras
• On the defining equations of Rees algebra of a height two perfect ideal using the theory of $D$-modules