Advanced Studies in Pure Mathematics

Resonance webs of hyperplane arrangements

Jorge Vitório Pereira

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Abstract

Each irreducible component of the first resonance variety of a hyperplane arrangement naturally determines a codimension one foliation on the ambient space. The superposition of these foliations define what we call the resonance web of the arrangement. In this paper we initiate the study of these objects with emphasis on their spaces of abelian relations.

Article information

Source
Arrangements of Hyperplanes — Sapporo 2009, H. Terao and S. Yuzvinsky, eds. (Tokyo: Mathematical Society of Japan, 2012), 261-291

Dates
Received: 31 March 2010
Revised: 24 December 2010
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543085012

Digital Object Identifier
doi:10.2969/aspm/06210261

Mathematical Reviews number (MathSciNet)
MR2933800

Zentralblatt MATH identifier
1261.52015

Subjects
Primary: 52C35: Arrangements of points, flats, hyperplanes [See also 32S22] 53A60: Geometry of webs [See also 14C21, 20N05]

Keywords
Web geometry abelian relations hyperplane arrangements resonance varieties

Citation

Pereira, Jorge Vitório. Resonance webs of hyperplane arrangements. Arrangements of Hyperplanes — Sapporo 2009, 261--291, Mathematical Society of Japan, Tokyo, Japan, 2012. doi:10.2969/aspm/06210261. https://projecteuclid.org/euclid.aspm/1543085012


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