location:  Publications → journals → CMB
Abstract view

Characteristic Varieties for a Class of Line Arrangements

Published:2010-08-09
Printed: Mar 2011
• Thi Anh Thu Dinh,
Laboratoire J. A. Dieudonné, Université de Nice Sophia Antipolis, Parc Valrose, 06108 Nice Cedex 02, France
 Format: HTML LaTeX MathJax PDF

Abstract

Let $\mathcal{A}$ be a line arrangement in the complex projective plane $\mathbb{P}^2$, having the points of multiplicity $\geq 3$ 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.
 Keywords: local system, line arrangement, characteristic variety, resonance variety
 MSC Classifications: 14C21 - Pencils, nets, webs [See also 53A60] 14F99 - None of the above, but in this section 32S22 - Relations with arrangements of hyperplanes [See also 52C35] 14E05 - Rational and birational maps 14H50 - Plane and space curves

 top of page | contact us | privacy | site map |