Admissibility of local systems for some classes of line arrangements (Q2925385)
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scientific article; zbMATH DE number 6359658
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Admissibility of local systems for some classes of line arrangements |
scientific article; zbMATH DE number 6359658 |
Statements
21 October 2014
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rank one local systems
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line arrangement
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characteristic variety
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resonance variety
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Admissibility of local systems for some classes of line arrangements (English)
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Let \(M\) be the complement of a line arrangement in the complex projective plane. A rank one local system \(L\) on \(M\) is admissible if the twisted cohomology groups \(H^*(M,L)\) can be computed using the Aomoto complex associated to the complex cohomology algebra \(H^*(M,C)\). The author gives a sufficient condition such that all the rank one local systems on \(M\) are admissible, of similar flavor as those given by \textit{T. A. T. Dinh} [Can. Math. Bull. 54, No. 1, 56--67 (2011; Zbl 1215.14011)]. This implies certain properties of the characteristic variety and resonance variety of \(M\).
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0.8966314792633057
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0.893121600151062
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0.8221791982650757
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0.7975179553031921
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