The group law on the tropical Hesse pencil
arXiv:1111.0131 · doi:10.1007/s13160-016-0226-8
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.
17 pages, 1 figure, submitted to Special Issue of the Journal Mathematics and Computers in Simulation on "Nonlinear Waves: Computation and Theory"