2016/06/06 by David Cook, David Cook II, Cook, David +2
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis #math.AC
paper · pdf · doi:10.48550/arxiv.1606.01809
22 pages. arXiv admin note: substantial text overlap with arXiv:1305.1314
arxiv created 2016/06/06 · openalex publication_date 2016/06/06 · arxiv updated 2016/06/07 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Deciding the presence of the weak Lefschetz property often is a challenging problem. In this work an in-depth study is carried out in the case of Artinian monomial ideals with four generators in three variables. We use a connection to lozenge tilings to describe semistability of the syzygy bundle of such an ideal, to determine its generic splitting type, and to decide the presence of the weak Lefschetz property. We provide results in both characteristic zero and positive characteristic.