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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