Year: 2026
Type: preprint
Abstract: In the 1980s, Stanley and J. Watanabe proved that over a field of characteristic zero every monomial complete intersection has the strong Lefschetz property. Determining which monomial complete intersections in positive characteristic have the weak Lefschetz property has been the subject of ongoing research. In this paper, we give a complete description of the locus of exponent vectors corresponding to monomial complete intersections over a field of positive characteristic that fail the weak Lefschetz property. We describe this locus explicitly in terms of translates of positive-orthant lattice balls in the taxicab metric.
Source: arXiv (Cornell University)
Author: LaClair, Adam
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W7214101305