English

Tropical curves, their Jacobians and Theta functions

Algebraic Geometry 2011-11-09 v2 Combinatorics

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.

Keywords

Cite

@article{arxiv.math/0612267,
  title  = {Tropical curves, their Jacobians and Theta functions},
  author = {Grigory Mikhalkin and Ilia Zharkov},
  journal= {arXiv preprint arXiv:math/0612267},
  year   = {2011}
}

Comments

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

R2 v1 2026-07-22T17:47:38.352Z