Ubiquity of complete intersection liaison classes

TL;DR

This paper introduces new invariants and methods to enumerate and distinguish large families of complete intersection liaison classes, revealing their widespread occurrence and structural properties.

Contribution

It develops a liaison invariant that commutes with hypersurface sections and applies it to classify liaison classes of projective schemes and ideals.

Findings

Liaison invariant that commutes with hypersurface sections

Obstructions to ruled joins sharing liaison classes

Enumeration of liaison classes of perfect ideals

Abstract

In this paper, we provide constructions to enumerate large numbers of CI-liaison classes. To this end, we introduce a liaison invariant and prove several results concerning it, notably that it commutes with hypersurface sections. This theory is applied to the CI-liaison classes of ruled joins of projective schemes, yielding strong obstructions for such joins to lie in the same liaison class. A second construction arises from the actions of automorphisms on liaison classes, allowing the enumeration of many liaison classes of perfect ideals of codimension at least three.