On the topology of arrangements of a cubic and its inflectional tangents. (English) Zbl 1429.14020

Summary: 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.


14H50 Plane and space curves
14H45 Special algebraic curves and curves of low genus
14F45 Topological properties in algebraic geometry
51H30 Geometries with algebraic manifold structure
14H52 Elliptic curves
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