Flops, Gromov-Witten invariants and symmetries of line bundle cohomology on Calabi-Yau three-folds

Callum R. Brodie (1) , Andrei Constantin , Andre Lukas

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

The zeroth line bundle cohomology on Calabi-Yau three-folds encodes information about the existence of flop transitions and the genus zero Gromov-Witten invariants. We illustrate this claim by studying several Picard number 2 Calabi-Yau three-folds realised as complete intersections in products of projective spaces. Many of these manifolds exhibit certain symmetries on the Picard lattice which preserve the zeroth cohomology.

Mots clés: Calabi-Yau; Cohomology; Gromov-Witten invariants; String theory; Symmetries; Line bundles; cohomology; lattice

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]

Callum R. Brodie, Andrei Constantin, Andre Lukas. Flops, Gromov-Witten invariants and symmetries of line bundle cohomology on Calabi-Yau three-folds. J.Geom.Phys., 2022, 171, pp.104398. ⟨10.1016/j.geomphys.2021.104398⟩. ⟨hal-02987451⟩