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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
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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 local system, line arrangement, characteristic variety, resonance variety
MSC Classifications: 14C21, 14F99, 32S22, 14E05, 14H50 show english descriptions Pencils, nets, webs [See also 53A60]
None of the above, but in this section
Relations with arrangements of hyperplanes [See also 52C35]
Rational and birational maps
Plane and space curves
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
 

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