Generalized Jouanolou duality, weakly Gorenstein rings, and applications to blowup algebras

TL;DR

This paper introduces a generalized Jouanolou duality applicable to a new class of rings called weakly Gorenstein, providing a framework to analyze blowup algebras and their defining equations.

Contribution

It extends Jouanolou duality to weakly Gorenstein rings, enabling new insights into blowup algebras and Rees algebra equations.

Findings

Established a new duality framework for weakly Gorenstein rings

Applied the theory to determine defining equations of Rees algebras

Provided tools for studying blowup algebras in broader contexts

Abstract

We provide a generalization of Jouanolou duality that is applicable to a plethora of situations. The environment where this generalized duality takes place is a new class of rings, that we introduce and call weakly Gorenstein. As a main consequence, we obtain a new general framework to investigate blowup algebras. We use our results to study and determine the defining equations of the Rees algebra of certain families of ideals.