Characteristic Varieties for a Class of Line Arrangements

Canadian mathematical bulletin

Thi Anh Thu Dinh¹ 

[1] Laboratoire J. A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France

关键词: local system;    line arrangement;    characteristic variety;    resonance variety;   

DOI  :  10.4153/CMB-2010-092-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $mathcal{A}$ be a line arrangement in the complex projective plane$mathbb{P}^2$, having the points of multiplicity $geq 3$ situated on twolines in $mathcal{A}$, say $H_0$ and $H_{infty}$. Then we show that thenon-local irreducible components of the first resonance variety$mathcal{R}_1(mathcal{A})$ are 2-dimensional and correspond to parallelograms $mathcal{P}$ in$mathbb{C}^2=mathbb{P}^2 setminus H_{infty}$ whose sides are in $mathcal{A}$ and forwhich $H_0$ is a diagonal.

【 授权许可】

Unknown