On Rees algebras of ideals and modules over hypersurface rings

TL;DR

This paper investigates the structure of Rees algebras for specific ideals and modules over hypersurface rings, providing minimal generators and analyzing algebraic properties like Cohen-Macaulayness.

Contribution

It offers a minimal generating set for Rees algebras of codimension 2 perfect ideals and describes Rees algebras of modules with projective dimension one over hypersurface rings.

Findings

Minimal generating sets for Rees algebras of codimension 2 perfect ideals.

Description of defining ideals of Rees algebras of modules with projective dimension one.

Criteria for Cohen-Macaulayness of these Rees algebras.

Abstract

The acquisition of the defining equations of Rees algebras is a natural way to study these algebras and allows certain invariants and properties to be deduced. In this paper, we consider Rees algebras of codimension 2 perfect ideals of hypersurface rings and produce a minimal generating set for their defining ideals. Then, using generic Bourbaki ideals, we study Rees algebras of modules with projective dimension one over hypersurface rings. We describe the defining ideal of such algebras and determine Cohen-Macaulayness and other invariants.