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1 June 2010 The tropical vertex
Mark Gross, Rahul Pandharipande, Bernd Siebert
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Duke Math. J. 153(2): 297-362 (1 June 2010). DOI: 10.1215/00127094-2010-025

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

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Mark Gross. Rahul Pandharipande. Bernd Siebert. "The tropical vertex." Duke Math. J. 153 (2) 297 - 362, 1 June 2010. https://doi.org/10.1215/00127094-2010-025

Information

Published: 1 June 2010
First available in Project Euclid: 26 May 2010

zbMATH: 1205.14069
MathSciNet: MR2667135
Digital Object Identifier: 10.1215/00127094-2010-025

Subjects:
Primary: 14N35
Secondary: 53D45

Rights: Copyright © 2010 Duke University Press

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Vol.153 • No. 2 • 1 June 2010
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