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

Pandharipande, R.; Pixton, A.

doi:10.1090/jams/858

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

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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