The Generic Initial Ideals of Powers of a 2-Complete Intersection

TL;DR

This paper develops algorithms to compute the reverse lexicographic generic initial ideals of powers of a 2-complete intersection ideal, providing a systematic approach based on the ideal's generators and their degrees.

Contribution

It introduces six algorithms tailored to compute generic initial ideals of powers of 2-complete intersection ideals, depending on the power and generator degrees.

Findings

Six algorithms for computing generic initial ideals

Algorithms adapt to different powers and generator degrees

Provides explicit methods for reverse lexicographic generic initial ideals

Abstract

We compute the reverse lexicographic generic initial ideals of the powers of a 2-complete intersection ideal I. In particular, we give six algorithms to compute these generic initial ideals, the choice of which depends on the power and on the relative degrees of the minimal generators of I.