Tropical curves, their Jacobians and Theta functions

Mathematics – Algebraic Geometry

Scientific paper

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

Scientific paper

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.

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