The linkage class of a grade three complete intersection

TL;DR

This paper provides a comprehensive classification and structural understanding of grade three licci ideals over fields of characteristic zero, extending previous results through advanced algebraic tools.

Contribution

It introduces new structure theorems for grade three licci ideals and classifies them up to deformation, expanding on earlier foundational work.

Findings

Complete classification of grade three licci ideals

Descriptions of minimal free resolutions for these ideals

Extension of earlier algebraic results by Buchsbaum-Eisenbud, Brown, and Sanchez

Abstract

Working over a field of characteristic zero, we give structure theorems for all grade three licci ideals and their minimal free resolutions. In particular, we completely classify such ideals up to deformation. The descriptions of their resolutions extend earlier results by Buchsbaum-Eisenbud, Brown, and Sanchez. Our primary tool is the theory of higher structure maps originating from the study of generic free resolutions of length three.