| |
|
Dun Liang
Invariants, bitangents, and matrix representations of plane quartics with 3-cyclic automorphisms
view
print
|
|
| Published: |
June 6, 2020. |
| Keywords: |
plane quartic, automorphism, bitangent, invariant. |
| Subject: |
14H37, 14Q05. |
|
|
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 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.
|
|
| Acknowledgements
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
liangdun@hynu.edu.cn
|
|
