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Nets in P^2 and Alexander Duality
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- Abdallah, Nancy (author)
- Högskolan i Borås,Akademin för textil, teknik och ekonomi
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- Schenck, Hal (author)
- Department of Mathematics, Auburn University, Auburn, AL, 36849, USA
- (creator_code:org_t)
- 2023
- 2023
- English.
- In: Discrete & Computational Geometry. - 0179-5376 .- 1432-0444.
- Journal article (peer-reviewed)
Abstract
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- A 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
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- ref (subject category)
- art (subject category)
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