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

Pandharipande, R.¹ ; Pixton, A.^2, 3

¹ Departement Mathematik, ETH Zürich, Zürich, Switzerland
² Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
³ Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Journal of the American Mathematical Society, Tome 30 (2017) no. 2, pp. 389-449

Résumé

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

Détail

DOI : 10.1090/jams/858

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