2022/08/02 by Nancy Abdallah, Abdallah, Nancy, Hal Schenck +1
Mathematics · #05B35 #52C35 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2208.01557
openalex publication_date 2022/08/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A net in ℙ2 is a configuration of lines \mathcal A and points X satisfying certain incidence properties. Nets appear in a variety of settings, ranging from quasigroups to combinatorial design to classification of Kac-Moody algebras to cohomology jump loci of hyperplane arrangements. For a matroid M and rank r, we associate a monomial ideal (a monomial variant of the Orlik-Solomon ideal) to the set of flats of M of rank ≤ r. In the context of line arrangements in ℙ2, applying Alexander duality to the resulting ideal yields insight into the combinatorial structure of nets.