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arXiv · 1705.02803

Connected numbers and the embedded topology of plane curves

Taketo Shirane
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Abstract

The splitting number of a plane irreducible curve for a Galois cover is effective to distinguish the embedded topologies of plane curves. In this paper, we define a connected number of any plane curve for a Galois cover whose branch divisor has no common components with the plane curve, which is similar to the splitting number. We classify the embedded topology of Artal arrangements of degree $b\geq 4$ by the connected number, where an Artal arrangement of degree $b$ is a plane curve consisting of one smooth curve of dgree $b$ and three total inflectional tangents.

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Taketo Shirane. 2017-05-08. Connected numbers and the embedded topology of plane curves. https://doi.org/10.4153/cmb-2017-066-5

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