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arXiv · 1902.02914

Invariants, Bitangents and Matrix Representations of Plane Quartics with 3-Cyclic Automorphisms

Dun Liang
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Abstract

In this work we compute the Dixmier invariants and bitangents of the plane quartics with 3,6 or 9-cyclic automorphisms, we find that a quartic curve with 6-cyclic automorphism will have 3 horizontal bitangents which form an asysgetic triple. We also discuss the linear matrix representation problem of such curves, and find a degree 6 equation of 1 variable which solves the symbolic solution of the linear matrix representation problem for the curve with 6-cyclic automorphism.

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Dun Liang. 2019-04-02. Invariants, Bitangents and Matrix Representations of Plane Quartics with 3-Cyclic Automorphisms. https://arxiv.org/abs/1902.02914

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