Proceedings of the Japan Academy, Series A, Mathematical Sciences

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

Shinzo Bannai, Benoît Guerville-Ballé, Taketo Shirane, and Hiro-o Tokunaga

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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.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 93, Number 6 (2017), 50-53.

First available in Project Euclid: 2 June 2017

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Zentralblatt MATH identifier

Primary: 14H50: Plane and space curves 14H45: Special curves and curves of low genus 14F45: Topological properties 51H30: Geometries with algebraic manifold structure [See also 14-XX]

Subarrangement Zariski pair $k$-Artal arrangement


Bannai, Shinzo; Guerville-Ballé, Benoît; Shirane, Taketo; Tokunaga, Hiro-o. On the topology of arrangements of a cubic and its inflectional tangents. Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 6, 50--53. doi:10.3792/pjaa.93.50.

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