Inductive and Recursive Freeness of Localizations of Multiarrangements

Torsten Hoge (), Gerhard Röhrle () and Anne Schauenburg ()
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Torsten Hoge: Leibniz Universität Hannover, Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Fakultät für Mathematik und Physik
Gerhard Röhrle: Ruhr-Universität Bochum, Fakultät für Mathematik
Anne Schauenburg: Ruhr-Universität Bochum, Fakultät für Mathematik

A chapter in Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory, 2017, pp 403-421 from Springer

Abstract: Abstract The class of free multiarrangements is known to be closed under taking localizations. We extend this result to the stronger notions of inductive and recursive freeness. As an application, we prove that recursively free (multi)arrangements are compatible with the product construction for (multi)arrangements. In addition, we show how our results can be used to derive that some canonical classes of free multiarrangements are not inductively free.

Keywords: Multiarrangement; Free arrangement; Inductively free arrangement; Recursively free arrangement; Localization of an arrangement; Primary 52C35, 14N20; Secondary 51D20 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-70566-8_16

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DOI: 10.1007/978-3-319-70566-8_16

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