The group law on a tropical elliptic curve

Abstract

In analogy with the classical group law on a plane cubic curve, we define a group law on a smooth plane tropical cubic curve. We show that the resulting group is isomorphic to $S^1$.

13 pages, latex2e, 5 figures as pstex and pstex_t files

Cited by in corpus (12)

• The Maslov dequantization, idempotent and tropical mathematics: A brief introduction
• Ultradiscretization of a solvable two-dimensional chaotic map associated with the Hesse cubic curve
• Jacobian varieties of reduced tropical curves
• An Ultradiscrete QRT mapping from Tropical Elliptic Curves
• Tropical conics for the layman
• Addition in Jacobians of tropical hyperelliptic curves
• Smooth tropical surfaces with infinitely many tropical lines
• Tropical orbit spaces and the moduli spaces of elliptic tropical curves
• On the addition formula for the tropical Hesse pencil
• A geometric realization of the ultradiscrete periodic Toda lattice via tropical plane curves
• Counting tropical elliptic plane curves with fixed j-invariant
• A note on tropical triangles in the plane