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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Descendant log Gromov-Witten invariants for toric varieties and tropical curves
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by Travis Mandel and Helge Ruddat PDF
Trans. Amer. Math. Soc. 373 (2020), 1109-1152 Request permission

Abstract:

Using degeneration techniques, we prove the correspondence of tropical curve counts and log Gromov-Witten invariants with general incidence and psi-class conditions in toric varieties for genus zero curves. For higher-genus situations, we prove the correspondence for the non-superabundant part of the invariant. We also relate the log invariants to the ordinary ones, in particular explaining the appearance of negative multiplicities in the descendant correspondence result of Mark Gross.
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Additional Information
  • Travis Mandel
  • Affiliation: School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
  • MR Author ID: 982182
  • ORCID: 0000-0003-3127-4429
  • Email: travis.mandel@ed.ac.uk
  • Helge Ruddat
  • Affiliation: JGU Mainz, Institut für Mathematik, Staudingerweg 9, 55128 Mainz, Germany
  • MR Author ID: 912430
  • Email: ruddat@uni-mainz.de
  • Received by editor(s): August 2, 2018
  • Received by editor(s) in revised form: June 20, 2019
  • Published electronically: October 18, 2019
  • Additional Notes: The first author was supported by the Center of Excellence Grant “Centre for Quantum Geometry of Moduli Spaces” from the Danish National Research Foundation (DNRF95) and later by the National Science Foundation RTG Grant DMS-1246989 and the Starter Grant “Categorified Donaldson-Thomas Theory” no. 759967 of the European Research Council.
    The second author was partially supported by the DFG Emmy Noether grant RU 1629/4-1 and DFG SFB TR 45.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 1109-1152
  • MSC (2010): Primary 14M25, 14N10, 14N35, 14T05
  • DOI: https://doi.org/10.1090/tran/7936
  • MathSciNet review: 4068259