New York Journal of Mathematics
Volume 26 (2020), 636-655


Dun Liang

Invariants, bitangents, and matrix representations of plane quartics with 3-cyclic automorphisms

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Published: June 6, 2020.
Keywords: plane quartic, automorphism, bitangent, invariant.
Subject: 14H37, 14Q05.

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 asyzygetic 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.


The author thanks the referee for a careful reading of this paper and for his suggestions. The author also thanks J.W. Hoffman of LSU for suggestions on this paper.

Author information

Dun Liang:
School of Mathematics and Statistics
Hengyang Normal University
Hengyang, Hunan 421002, China