an:06723457
Zbl 1362.14066
Nobe, Atsushi
Group actions on the tropical Hesse pencil
EN
Japan J. Ind. Appl. Math. 33, No. 3, 537-556 (2016).
00361829
2016
j
14T05 14H52 37P99
Hesse pencil; Hessian group; QRT system; theta function; tropical curve; ultradiscretization
Summary: Addition of points on the tropical Hesse curve is realized via its intersections with two tropical lines. Then the addition formula for the points on the curve is reduced from the one for the level-three theta functions through the ultradiscretization procedure. In addition, a tropical analogue of the Hessian group \(G_{216}\), the group of linear automorphisms acting on the Hesse pencil, is investigated; it is shown that the dihedral group \(\mathcal {D}_3\) of degree three is the group of linear automorphisms acting on the tropical Hesse pencil.