## Tropical Jacobians in {\large$\mathbb{R}^2$}

J. Math. Sci. Univ. Tokyo
Vol. 17 (2010), No. 2, Page 135--157.

Yoshitomi, Shuhei
Tropical Jacobians in {\large$\mathbb{R}^2$}
[Full Article (PDF)] [MathSciNet Review (HTML)] [MathSciNet Review (PDF)]

Abstract:
By tropical Abel-Jacobi theorem, the Jacobian of a tropical curve is isomorphic to the Picard group. A tropical curve in $\mathbb{R}^2$ corresponds to an immersion from a tropical curve to $\mathbb{R}^2$. In this paper, we show that any principal divisor on a tropical curve is the restriction of a principal divisor on the ambient plane $\mathbb{R}^2$.

Keywords: Cartan decomposition, visible action, symmetric space, herringbone stitch, spherical variety.

Mathematics Subject Classification (2010): Primary 14T05; Secondary 52B20.