On the structure of monomial complete intersections in positive characteristic

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.

References in corpus (2)

• On the Hilbert series of ideals generated by generic forms
• The strong Lefschetz property of monomial complete intersections in two variables

Cited by in corpus (4)

• The strong Lefschetz property of monomial complete intersections in two variables
• Forcing the weak Lefschetz property for equigenerated monomial ideals
• Roller Coaster Gorenstein algebras and Koszul algebras failing the weak Lefschetz property
• Limit $F$-signature functions of two-variable binomial hypersurfaces