Geodesic
Two-graphs and the Embedded Topology of Smooth Quartics and its Bitangent Lines
Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 802-812

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DOI

In this paper, we study how to distinguish the embedded topology of a smooth quartic and its bitangent lines. In order to do this, we introduce the concept of two-graphs and switching classes from graph theory. This new method improves previous results about a quartic and three bitangent lines considered by E. Artal Bartolo and J. Vallès, four bitangent lines considered by the authors and H. Tokunaga, and enables us to distinguish the embedded topology of a smooth quartic and five or more bitangent lines. As an application, we obtain a new Zariski 5-tuple and a Zariski 9-tuple for arrangements consisting of a smooth quartic and five of its bitangent lines and six of its bitangent lines, respectively.
DOI : 10.4153/S0008439520000053
Mots-clés : Zariski pair, embedded topology, two-graph, smooth quartic, bitangent line 
Bannai, Shinzo; Ohno, Momoko. Two-graphs and the Embedded Topology of Smooth Quartics and its Bitangent Lines. Canadian mathematical bulletin, Tome 63 (2020) no. 4, pp. 802-812. doi: 10.4153/S0008439520000053
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