The quadratic complete intersections with the action of the symmetric group

TL;DR

This paper proves that quadratic complete intersections with symmetric group actions possess the strong Lefschetz property over characteristic zero fields, and constructs new classes of such intersections with higher degree generators.

Contribution

It establishes the strong Lefschetz property for quadratic complete intersections with symmetric group actions and introduces new classes with higher degree generators.

Findings

Quadratic complete intersections with symmetric group actions have the strong Lefschetz property.

New classes of homogeneous complete intersections with higher degree generators also have this property.

The results hold over fields of characteristic zero.

Abstract

We prove that any quadratic complete intersection with certain action of the symmetric group has the strong Lefschetz property over a field of characteristic zero. As a consequence of it we construct a new class of homogeneous complete intersections with generators of higher degrees which have the strong Lefschetz property.