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

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- by R. Pandharipande and A. Pixton PDF
- J. Amer. Math. Soc.
**30**(2017), 389-449 Request permission

## 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 $q \leftrightarrow q^{-1}$.## References

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## Additional Information

**R. Pandharipande**- Affiliation: Departement Mathematik, ETH Zürich, Zürich, Switzerland
- MR Author ID: 357813
- 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
- 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: https://doi.org/10.1090/jams/858
- MathSciNet review: 3600040