Hyperplane arrangements and Milnor fibrations

Alexander I. Suciu

Annales de la faculté des sciences de Toulouse Mathématiques (2014)

  • Volume: 23, Issue: 2, page 417-481
  • ISSN: 0240-2963

Abstract

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There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank 1 local systems on the complement of the arrangement to gain information on the homology of the other three spaces, and on the monodromy operators of the various fibrations.

How to cite

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Suciu, Alexander I.. "Hyperplane arrangements and Milnor fibrations." Annales de la faculté des sciences de Toulouse Mathématiques 23.2 (2014): 417-481. <http://eudml.org/doc/275363>.

@article{Suciu2014,
abstract = {There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank $1$ local systems on the complement of the arrangement to gain information on the homology of the other three spaces, and on the monodromy operators of the various fibrations.},
author = {Suciu, Alexander I.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {arrangements of hyperplanes; central arrangement; Milnor fibration; cohomology jump loci; characteristic variety; resonance variety},
language = {eng},
month = {3},
number = {2},
pages = {417-481},
publisher = {Université Paul Sabatier, Toulouse},
title = {Hyperplane arrangements and Milnor fibrations},
url = {http://eudml.org/doc/275363},
volume = {23},
year = {2014},
}

TY - JOUR
AU - Suciu, Alexander I.
TI - Hyperplane arrangements and Milnor fibrations
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2014/3//
PB - Université Paul Sabatier, Toulouse
VL - 23
IS - 2
SP - 417
EP - 481
AB - There are several topological spaces associated to a complex hyperplane arrangement: the complement and its boundary manifold, as well as the Milnor fiber and its own boundary. All these spaces are related in various ways, primarily by a set of interlocking fibrations. We use cohomology with coefficients in rank $1$ local systems on the complement of the arrangement to gain information on the homology of the other three spaces, and on the monodromy operators of the various fibrations.
LA - eng
KW - arrangements of hyperplanes; central arrangement; Milnor fibration; cohomology jump loci; characteristic variety; resonance variety
UR - http://eudml.org/doc/275363
ER -

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