Characteristic Varieties for a Class of Line Arrangements

Dinh, Thi Anh Thu

Canadian mathematical bulletin, Tome 54 (2011) no. 1, pp. 56-67

Résumé

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.

Détail

DOI : 10.4153/CMB-2010-092-6

Mots-clés : 14C21, 14F99, 32S22, 14E05, 14H50, local system, line arrangement, characteristic variety, resonance variety