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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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Gromov-Witten/Pairs correspondence for the quintic 3-fold
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by R. Pandharipande and A. Pixton
J. Amer. Math. Soc. 30 (2017), 389-449
Published electronically: March 17, 2016


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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Bibliographic Information
  • R. Pandharipande
  • Affiliation: Departement Mathematik, ETH Zürich, Zürich, Switzerland
  • MR Author ID: 357813
  • Email:
  • 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:
  • 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.
  • © Copyright 2016 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 30 (2017), 389-449
  • MSC (2010): Primary 14N35; Secondary 14H60
  • DOI:
  • MathSciNet review: 3600040