Duke Mathematical Journal

Toric degenerations of toric varieties and tropical curves

Takeo Nishinou and Bernd Siebert

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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

Article information

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

Dates
First available in Project Euclid: 26 September 2006

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

Subjects
Primary: 14N10: Enumerative problems (combinatorial problems)
Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20] 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]

Citation

Nishinou, Takeo; Siebert, Bernd. Toric degenerations of toric varieties and tropical curves. Duke Mathematical Journal 135 (2006), no. 1, 1--51. doi:10.1215/S0012-7094-06-13511-1. http://projecteuclid.org/euclid.dmj/1159281063.


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