Toric degenerations of toric varieties and tropical curves
Algebraic Geometry
2007-05-23 v3
Abstract
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.
Keywords
Cite
@article{arxiv.math/0409060,
title = {Toric degenerations of toric varieties and tropical curves},
author = {Takeo Nishinou and Bernd Siebert},
journal= {arXiv preprint arXiv:math/0409060},
year = {2007}
}
Comments
41 pages, 3 figures; (v3: Multiplicity definition and Prop.6.3 corrected, Example 9.2,(4) added)