Takeo Nishinou, Bernd Siebert. Toric Degenerations of Toric Varieties and Tropical Curves. Duke Mathematical Journal. 2006.
Abstract
We show that the counting of rational curves on a complete toric variety which are in general position relative 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