Invariants, Bitangents and Matrix Representations of Plane Quartics with 3-Cyclic Automorphisms. (arXiv:1902.02914v2 [math.AG] UPDATED)

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. 查看全文>>