English

The group law on the tropical Hesse pencil

Exactly Solvable and Integrable Systems 2018-02-06 v1

Abstract

We show that the addition of points on the tropical Hesse curve can be realized via the intersection with a tropical line. Then the addition formula for the tropical Hesse curve is reduced from those for the level-three theta functions through the ultradiscretization procedure. A tropical analogue of the Hessian group, the group of linear automorphisms acting on the Hesse pencil, is also investigated; it is shown that the dihedral group of degree three is the group of linear automorphisms acting on the tropical Hesse pencil.

Keywords

Cite

@article{arxiv.1111.0131,
  title  = {The group law on the tropical Hesse pencil},
  author = {Atsushi Nobe},
  journal= {arXiv preprint arXiv:1111.0131},
  year   = {2018}
}

Comments

17 pages, 1 figure, submitted to Special Issue of the Journal Mathematics and Computers in Simulation on "Nonlinear Waves: Computation and Theory"