On the admissibility of certain local systems

A rank one local system on the complement of a hyperplane arrangement is said to be admissible if it satisfies certain non-positivity condition at every resonant edges. It is known that the cohomology of admissible local system can be computed combinatorially. In this paper, we study the structure o...

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Bibliographic Details
Published inTopology and its applications Vol. 178; pp. 288 - 299
Main Authors Nazir, Shaheen, Torielli, Michele, Yoshinaga, Masahiko
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2014
Subjects
Admissible local systems
Characteristic variety
Line arrangements
14F99
Admissible local systems
32S22
Characteristic variety
Line arrangements
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Summary:A rank one local system on the complement of a hyperplane arrangement is said to be admissible if it satisfies certain non-positivity condition at every resonant edges. It is known that the cohomology of admissible local system can be computed combinatorially. In this paper, we study the structure of the set of all non-admissible local systems in the character torus. We prove that the set of non-admissible local systems forms a union of subtori. The relations with characteristic varieties are also discussed.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2014.10.001