Arkiv för Matematik

Volume 56 (2018)

Number 2

Determining all $(2, 3)$-torus structures of a symmetric plane curve

Pages: 341 – 349



Remke Kloosterman (Dipartimento di Matematica, Università degli Studi di Padova, Italy)


In this paper, we describe all $(2, 3)$-torus structures of a highly symmetric $39$-cuspidal degree $12$ curve.

A direct computer-aided determination of these torus structures seems to be out of reach. We use various quotients by automorphisms to find torus structures. We use a height pairing argument to show that there are no further structures.

The author has been supported by the GNSAGA of INDAM. The author gratefully thanks Carel Faber, Matthias Schütt and the referee for the constructive comments and recommendations which definitely helped to improve the readability of the paper.

Received 26 January 2017

Received revised 9 January 2018

Accepted 8 February 2018

Published 24 May 2022