# Toric degenerations of toric varieties and tropical curves

@article{Nishinou2004ToricDO, title={Toric degenerations of toric varieties and tropical curves}, author={Takeo Nishinou and Bernd S Siebert}, journal={Duke Mathematical Journal}, year={2004}, volume={135}, pages={1-51} }

We show that the counting of rational curves on a complete toric variety that are in general position to the toric prime divisors coincides with the counting of certain tropical curves. The proof is algebraic-geometric and relies on degeneration techniques and log deformation theory. This generalizes results of Mikhalkin obtained by different methods in the surface case to arbitrary dimensions.

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