Characteristic varieties for a class of line arrangements

Abstract

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 $\mathcal{P}$ in ${\mathbb{C}}^2={\mathbb{P}}^2\setminus H_{\infty }$ whose sides are in $\mathcal{A}$ and for which $H_0$ is a diagonal.

12 pages, 1 figure

References in corpus (2)

• Algebraic invariants for right-angled Artin groups
• Toric complexes and Artin kernels