Three takes on almost complete intersection ideals of grade 3

TL;DR

This paper explores the structure of almost complete intersection ideals of grade 3 through three different constructions, including algebraic, equivariant, and geometric perspectives, providing new insights into their resolutions.

Contribution

It introduces three novel constructions of these ideals and their free resolutions, linking algebraic, equivariant, and geometric approaches.

Findings

Three distinct constructions of almost complete intersection ideals of grade 3.

A canonical form derived from equivariant construction.

An interpretation involving open sets in Schubert varieties.

Abstract

We are interested in the structure of almost complete intersection ideals of grade 3. We give three constructions of these ideals and their free resolutions: one from the commutative algebra point of view, an equivariant construction giving a nice canonical form, andfinally an interpretation in terms of open sets in certain Schubert varieties.