On the structure of monomial complete intersections in positive characteristic

TL;DR

This paper classifies when monomial complete intersections in positive characteristic have the strong Lefschetz property, confirming a conjecture and extending previous results on the weak Lefschetz property.

Contribution

It provides a complete classification of the strong Lefschetz property for monomial complete intersections with three or more variables and extends criteria for the weak Lefschetz property.

Findings

Complete classification of strong Lefschetz property in the case of ≥3 variables.

Extended the weak Lefschetz property results to finite residue fields.

Provided new sufficient criteria for Lefschetz properties.

Abstract

In this paper we study the Lefschetz properties of monomial complete intersections in positive characteristic. We give a complete classification of the strong Lefschetz property when the number of variables is at least three, which proves a conjecture by Cook II. We also extend earlier results on the weak Lefschetz property by dropping the assumption on the residue field being infinite, and by giving new sufficient criteria.