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.
On the topology of arrangements of a cubic and its inflectional tangents / Bannai, Shinzo; Guerville-Ballé, Benoît; Shirane, Taketo; Tokunaga, Hiro-o. - In: PROCEEDINGS OF THE JAPAN ACADEMY. SERIES A MATHEMATICAL SCIENCES. - ISSN 0386-2194. - 93:6(2017), pp. 50-53. [10.3792/pjaa.93.50]
On the topology of arrangements of a cubic and its inflectional tangents
Guerville-Ballé, Benoît;
2017-01-01
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
