Toric degenerations of toric varieties and tropical curves

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Toric degenerations of toric varieties and tropical curves

Takeo Nishinou and Bernd Siebert

Source: Duke Math. J. Volume 135, Number 1 (2006), 1-51.

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

Primary Subjects: 14N10

Secondary Subjects: 14M25, 14N35

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1159281063
Digital Object Identifier: doi:10.1215/S0012-7094-06-13511-1
Mathematical Reviews number (MathSciNet): MR2259922
Zentralblatt MATH identifier: 1105.14073

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