Group actions on the tropical Hesse pencil

Atsushi Nobe*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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 G216, the group of linear automorphisms acting on the Hesse pencil, is investigated; it is shown that the dihedral group D3 of degree three is the group of linear automorphisms acting on the tropical Hesse pencil.

Original languageEnglish
Pages (from-to)537-556
Number of pages20
JournalJapan Journal of Industrial and Applied Mathematics
Volume33
Issue number3
DOIs
Publication statusPublished - 2016 Dec 1
Externally publishedYes

Keywords

  • Hesse pencil
  • Hessian group
  • QRT system
  • Theta function
  • Tropical curve
  • Ultradiscretization

ASJC Scopus subject areas

  • Engineering(all)
  • Applied Mathematics

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