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

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[superscript iu] invariant under q ↔ q[subscript -1].