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Gromov-Witten/Pairs correspondence for the quintic 3-fold


Authors: R. Pandharipande and A. Pixton
Journal: J. Amer. Math. Soc. 30 (2017), 389-449
MSC (2010): Primary 14N35; Secondary 14H60
DOI: https://doi.org/10.1090/jams/858
Published electronically: March 17, 2016
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Abstract: We use the Gromov-Witten/Pairs (GW/P) descendent correspondence for toric 3-folds and degeneration arguments to establish the GW/P correspondence for several compact Calabi-Yau (CY) 3-folds (including all CY complete intersections in products of projective spaces). A crucial aspect of the proof is the study of the GW/P correspondence for descendents in relative geometries. Projective bundles over surfaces relative to a section play a special role. The GW/P correspondence for Calabi-Yau complete intersections provides a structure result for the Gromov-Witten invariants in a fixed curve class. After a change of variables, the Gromov-Witten series is a rational function in the variable $ -q=e^{iu}$ invariant under $ q \leftrightarrow q^{-1}$.


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Additional Information

R. Pandharipande
Affiliation: Departement Mathematik, ETH Zürich, Zürich, Switzerland
Email: rahul@math.ethz.ch

A. Pixton
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
Address at time of publication: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
Email: apixton@mit.edu

DOI: https://doi.org/10.1090/jams/858
Received by editor(s): August 25, 2014
Received by editor(s) in revised form: January 23, 2016, and February 7, 2016
Published electronically: March 17, 2016
Additional Notes: The first author was partially supported by NSF Grant DMS-1001154, SNF Grant 200021-143274, SNF Grant 200020-162928, SwissMAP, and ERC Grant AdG-320368-MCSK
The second author was supported by a NDSEG graduate fellowship.
Article copyright: © Copyright 2016 American Mathematical Society