Connected Numbers and the Embedded Topology of Plane Curves

Shirane, Taketo

Canadian mathematical bulletin, Tome 61 (2018) no. 3, pp. 650-658

Résumé

The splitting number of a plane irreducible curve for a Galois cover is effective in distinguishing the embedded topology of plane curves. In this paper, we define the connected number of a plane curve (possibly reducible) for a Galois cover, which is similar to the splitting number. By using the connected number, we distinguish the embedded topology of Artal arrangements of degree $b\,\ge \,4$ , where an Artal arrangement of degree $b$ is a plane curve consisting of one smooth curve of degree $b$ and three of its total inflectional tangents.

Détail

DOI : 10.4153/CMB-2017-066-5

Mots-clés : 14H30, 14H50, 14F45, plane curve, splitting curve, Zariski pair, cyclic cover, splitting number

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