On the topology of the Milnor fibration of a hyperplane arrangement

This note is mostly an expository survey, centered on the topology of complements of hyperplane arrangements, their Milnor fibrations, and their boundary structures. An important tool in this study is provided by the degree 1 resonance and characteristic varieties of the complement, and their tight...

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Bibliographic Details
Published inarXiv.org
Main Author Suciu, Alexandru I
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 14.03.2017
Subjects
Combinatorial analysis
Hyperplanes
Topology
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Summary:This note is mostly an expository survey, centered on the topology of complements of hyperplane arrangements, their Milnor fibrations, and their boundary structures. An important tool in this study is provided by the degree 1 resonance and characteristic varieties of the complement, and their tight relationship with orbifold fibrations and multinets on the underlying matroid. In favorable situations, this approach leads to a combinatorial formula for the first Betti number of the Milnor fiber and the algebraic monodromy. We also produce a pair of arrangements for which the respective Milnor fibers have the same Betti numbers, yet are not homotopy equivalent: the difference is picked up by isolated torsion points in the higher-depth characteristic varieties.
ISSN:2331-8422