Toric degenerations of toric varieties and tropical curves

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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

Keywords

Algebraic Geometry, 14N10; 14M25; 14N35

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/100857

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0409060
 http://arxiv.org/abs/math/0409060

Collections

arXiv