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Connected numbers and the embedded topology of plane curves

  • Taketo Shirane,
    National Institute of Technology, Ube College, Tokiwadai 2-14, Ube 755-8555, Japan
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Abstract

The splitting number of a plane irreducible curve for a Galois cover is effective to distinguish 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 $b\geq 4$, 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 tangen
Keywords: plane curve, splitting curve, Zariski pair, cyclic cover, splitting number plane curve, splitting curve, Zariski pair, cyclic cover, splitting number
MSC Classifications: 14H30, 14H50, 14F45 show english descriptions Coverings, fundamental group [See also 14E20, 14F35]
Plane and space curves
Topological properties
14H30 - Coverings, fundamental group [See also 14E20, 14F35]
14H50 - Plane and space curves
14F45 - Topological properties
 

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