Tropical curves, their Jacobians and Theta functions

Abstract

We study Jacobian varieties for tropical curves. These are real tori equipped with integral affine structure and symmetric bilinear form. We define tropical counterpart of the theta function and establish tropical versions of the Abel-Jacobi, Riemann-Roch and Riemann theta divisor theorems.

Journal version. Errors corrected, proofs improved, references added. 32 pages, 11 figures