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Characteristic Varieties for a Class of Line Arrangements

  • Thi Anh Thu Dinh (a1)

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 $P$ 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.

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References

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Characteristic Varieties for a Class of Line Arrangements

  • Thi Anh Thu Dinh (a1)

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