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arXiv · 1607.07618

On the topology of arrangements of a cubic and its inflectional tangents

Shinzo Bannai·Benoît Guerville-Ballé·Taketo Shirane·Hiro-o Tokunaga
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Abstract

A $k$-Artal arrangement is a reducible algebraic curve composed of a smooth cubic and $k$ inflectional tangents. By studying the topological properties of their subarrangements, we prove that for $k=3,4,5,6$, there exist Zariski pairs of $k$-Artal arrangements. These Zariki pairs can be distinguished in a geometric way by the number of collinear triples in the set of singular points contained in the cubic.

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Shinzo Bannai, Benoît Guerville-Ballé, Taketo Shirane, Hiro-o Tokunaga. 2016-07-26. On the topology of arrangements of a cubic and its inflectional tangents. https://arxiv.org/abs/1607.07618

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