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Transactions of the American Mathematical Society

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

 
 

 

Descendant log Gromov-Witten invariants for toric varieties and tropical curves


Authors: Travis Mandel and Helge Ruddat
Journal: Trans. Amer. Math. Soc. 373 (2020), 1109-1152
MSC (2010): Primary 14M25, 14N10, 14N35, 14T05
DOI: https://doi.org/10.1090/tran/7936
Published electronically: October 18, 2019
MathSciNet review: 4068259
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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.
Article copyright: © Copyright 2019 American Mathematical Society