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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.

MSC:

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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