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Connected Numbers and the Embedded Topology of Plane Curves

Published online by Cambridge University Press:  20 November 2018

Taketo Shirane
Taketo Shirane*
Affiliation:
National Institute of Technology, Ube College, Tokiwadai 2-14, Ube 755-8555, Japan, e-mail: tshirane@ube-k.ac.jp
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Abstract

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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.

Keywords

14H3014H5014F45plane curvesplitting curveZariski paircyclic coversplitting number
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 3 , 01 September 2018 , pp. 650 - 658
Copyright
Copyright © Canadian Mathematical Society 2018

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