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Characteristic Varieties for a Class of Line Arrangements

Published online by Cambridge University Press:  20 November 2018

Thi Anh Thu Dinh
Thi Anh Thu Dinh*
Affiliation:
Laboratoire J. A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, Francee-mail: dinh@unice.fr
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Abstract

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Let $\mathcal{A}$ be a line arrangement in the complex projective plane ${{\mathbb{P}}^{2}}$, having the points of multiplicity $\ge \,3$ situated on two lines in $\mathcal{A}$, say ${{H}_{0}}$ and ${{H}_{\infty }}$. Then we show that the non-local irreducible components of the first resonance variety ${{\mathcal{R}}_{1}}(\mathcal{A})$ are 2-dimensional and correspond to parallelograms $P$ in ${{\mathbb{C}}^{2}}={{\mathbb{P}}^{2}}\text{ }\backslash \text{ }{{H}_{\infty }}$ whose sides are in $\mathcal{A}$ and for which ${{H}_{0}}$ is a diagonal.

Keywords

14C2114F9932S2214E0514H50local systemline arrangementcharacteristic varietyresonance variety
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 54 , Issue 1 , 01 March 2011 , pp. 56 - 67
Copyright
Copyright © Canadian Mathematical Society 2011

References

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