The equations of Rees algebras of height three Gorenstein ideals in hypersurface rings

TL;DR

This paper characterizes the defining equations of Rees algebras for height three Gorenstein ideals in hypersurface rings, introduces a modified Jacobian dual, and examines algebraic properties like Cohen-Macaulayness.

Contribution

It provides a minimal generating set for the defining ideal of these Rees algebras using a new recursive algorithm and a modified Jacobian dual.

Findings

Explicit minimal generators for the defining ideal

Conditions for Cohen-Macaulayness of the Rees algebra

Bounds on Castelnuovo-Mumford regularity

Abstract

We study the Rees algebra of a perfect Gorenstein ideal of codimension 3 in a hypersurface ring. We provide a minimal generating set of the defining ideal of these rings by introducing a modified Jacobian dual and applying a recursive algorithm. Once the defining equations are known, we explore properties of these Rees algebras such as Cohen-Macaulayness and Castelnuovo-Mumford regularity.