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Nets in P^2 and Alexander Duality
University of Borås, Faculty of Textiles, Engineering and Business.ORCID iD: 0000-0002-8001-6787
Department of Mathematics, Auburn University, Auburn, AL, 36849, USA.
2023 (English)In: Discrete & Computational Geometry, ISSN 0179-5376, E-ISSN 1432-0444Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2023.
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Mathematics
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URN: urn:nbn:se:hb:diva-29866DOI: 10.1007/s00454-023-00504-1ISI: 000977047600001Scopus ID: 2-s2.0-85153409489OAI: oai:DiVA.org:hb-29866DiVA, id: diva2:1762723
Available from: 2023-06-05 Created: 2023-06-05 Last updated: 2024-02-01Bibliographically approved

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Abdallah, Nancy

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