Toric degenerations of toric varieties and tropical curves

Takeo Nishinou; Bernd Siebert

doi:10.1215/S0012-7094-06-13511-1

Toric degenerations of toric varieties and tropical curves

Takeo Nishinou, Bernd Siebert

Research output: Contribution to journal › Article › peer-review

109 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1-52
Number of pages	52
Journal	Duke Mathematical Journal
Volume	135
Issue number	1
DOIs	https://doi.org/10.1215/S0012-7094-06-13511-1
Publication status	Published - 2006 Oct 1
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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10.1215/S0012-7094-06-13511-1

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Toric degenerations of toric varieties and tropical curves

Abstract

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