Duke Mathematical Journal

The tropical vertex

Mark Gross, Rahul Pandharipande, and Bernd Siebert

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Abstract

Elements of the tropical vertex group are formal families of symplectomorphisms of the 2-dimensional algebraic torus. We prove that ordered product factorizations in the tropical vertex group are equivalent to calculations of certain genus zero relative Gromov-Witten invariants of toric surfaces. The relative invariants which arise have full tangency to a toric divisor at a single unspecified point. The method uses scattering diagrams, tropical curve counts, degeneration formulas, and exact multiple cover calculations in orbifold Gromov-Witten theory

Article information

Source
Duke Math. J., Volume 153, Number 2 (2010), 297-362.

Dates
First available in Project Euclid: 26 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1274902082

Digital Object Identifier
doi:10.1215/00127094-2010-025

Mathematical Reviews number (MathSciNet)
MR2667135

Zentralblatt MATH identifier
1205.14069

Subjects
Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 53D45: Gromov-Witten invariants, quantum cohomology, Frobenius manifolds [See also 14N35]

Citation

Gross, Mark; Pandharipande, Rahul; Siebert, Bernd. The tropical vertex. Duke Math. J. 153 (2010), no. 2, 297--362. doi:10.1215/00127094-2010-025. https://projecteuclid.org/euclid.dmj/1274902082


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