Nets in ℙ^2 and Alexander Duality
Discrete & Computational Geometry(2023)
摘要
net in ℙ^2 is a configuration of lines 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 ℙ^2 , applying Alexander duality to the resulting ideal yields insight into the combinatorial structure of nets.
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关键词
Line arrangement, Net, Alexander duality, Free resolution, 05B35, 52C35
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