Proc. Japan Acad. Ser. A Math. Sci. 93 (6), 50-53, (June 2017) DOI: 10.3792/pjaa.93.50
Shinzo Bannai, Benoît Guerville-Ballé, Taketo Shirane, Hiro-o Tokunaga
KEYWORDS: Subarrangement, Zariski pair, $k$-Artal arrangement, 14H50, 14H45, 14F45, 51H30
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 Zariski pairs can be distinguished in a geometric way by the number of collinear triples in the set of singular points of the arrangement contained in the cubic.