Generic initial ideal for complete intersections of embedding dimension three with strong Lefschetz property

TL;DR

This paper computes the generic initial ideal for certain three-dimensional complete intersections with the strong Lefschetz property, proving Moreno's conjecture in this case by showing it is almost reverse lexicographic.

Contribution

It introduces a method to determine the generic initial ideal for three-dimensional complete intersections with the strong Lefschetz property, confirming Moreno's conjecture for n=3.

Findings

Generic initial ideal is almost reverse lexicographic

Proof of Moreno's conjecture for n=3

Characterization of ideals with strong Lefschetz property

Abstract

We compute the generic initial ideal of a complete intersection of embedding dimension three with strong Lefschetz property and we show that it is an almost reverse lexicographic ideal. This enable us to give a proof for Moreno's conjecture in the case $n=3$.