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2020•Proceedings of the Japan Academy Series A Mathematical SciencesOpen access

Zariski tuples for a smooth cubic and its tangent lines

Shinzo Bannai, Hiro‐o Tokunaga

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Abstract

In this paper, we study the geometry of two-torsion points of elliptic curves in order to distinguish the embedded topology of reducible plane curves consisting of a smooth cubic and its tangent lines. As a result, we obtain a new family of Zariski tuples consisting of such curves.

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What this paper is about

In this paper, we study the geometry of two-torsion points of elliptic curves in order to distinguish the embedded topology of reducible plane curves consisting of a smooth cubic and its tangent lines. As a result, we obtain a new family of Zariski tuples consisting of such curves.

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OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, we study the geometry of two-torsion points of elliptic curves in order to distinguish the embedded topology of reducible plane curves consisting of a smooth cubic and its tangent lines. As a result, we obtain a new family of Zariski tuples consisting of such curves.

Key concepts: Tangent, Tuple, Torsion (gastropod), Mathematics, Tangent space, Geometry, Tangent vector, Pure mathematics

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