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

TL;DR

This paper proves the Gromov-Witten/Pairs correspondence for several Calabi-Yau 3-folds, including complete intersections, using degeneration techniques and relative geometry analysis, revealing rationality and symmetry properties of their invariants.

Contribution

It establishes the GW/P correspondence for compact Calabi-Yau 3-folds, extending previous results to new geometries via degeneration and relative geometry methods.

Findings

GW/P correspondence holds for several Calabi-Yau 3-folds.

Gromov-Witten series are rational functions invariant under q => 1/q.

Provides a structure result for Gromov-Witten invariants in fixed classes.

Abstract

We use the Gromov-Witten/Pairs descendent correspondence for toric 3-folds and degeneration arguments to establish the GW/P correspondence for several compact Calabi-Yau 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 change of variables, the Gromov-Witten series is a rational function in the variable -q=exp(iu) invariant under q => 1/q.