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arXiv · 1411.2653

Combinatorics of line arrangements and polynomial vector fields

Benoît Guerville-Ballé·Juan Viu-Sos
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Abstract

Let $\mathcal{A}$ be a real line arrangement and $\mathcal{D}(\mathcal{A})$ the module of $\mathcal{A}$-derivations view as the set of polynomial vector fields which possess $\mathcal{A}$ as an invariant set. We first characterize polynomial vector fields having an infinite number of invariant lines. Then we prove that the minimal degree of polynomial vector fields fixing only a finite set of lines in $\mathcal{D}(\mathcal{A})$ is not determined by the combinatorics of $\mathcal{A}$.

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Benoît Guerville-Ballé, Juan Viu-Sos. 2014-11-10. Combinatorics of line arrangements and polynomial vector fields. https://arxiv.org/abs/1411.2653

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