Toric degenerations of toric varieties and tropical curves

Details Toric degenerations of toric varieties and tropical curves Toric degenerations of toric varieties and tropical curves

2004-09-04

arxiv.org/abs/math/0409060v3

Mathematics

Algebraic Geometry

41 pages, 3 figures; (v3: Multiplicity definition and Prop.6.3 corrected, Example 9.2,(4) added)

Scientific paper

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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