Let be a height two ideal minimally generated by three homogeneous polynomials of the same degree , where is a field of characteristic zero. We use the theory of -modules to deduce information about the defining equations of the Rees algebra of . Let be the kernel of the canonical map from the symmetric algebra of onto the Rees algebra of . We prove that can be described as the solution set of a system of differential equations, that the whole bigraded structure of is characterized by the integral roots of certain -functions, and that certain de Rham cohomology groups can give partial information about .
Yairon Cid-Ruiz. "A -modules approach on the equations of the Rees algebra." J. Commut. Algebra 14 (2) 155 - 176, Summer 2022. https://doi.org/10.1216/jca.2022.14.155