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# Connected numbers and the embedded topology of plane curves

Published:2017-12-02

• Taketo Shirane,
National Institute of Technology, Ube College, Tokiwadai 2-14, Ube 755-8555, Japan
 Format: LaTeX MathJax PDF

## 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
 MSC Classifications: 14H30 - Coverings, fundamental group [See also 14E20, 14F35] 14H50 - Plane and space curves 14F45 - Topological properties

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