A Conjectural Formula for Genus One Gromov-Witten Invariants of a Class of Local Calabi-Yau n-folds

Abstract

We conjecture a formula for the generating function of genus one Gromov-Witten invariants of the local Calabi-Yau manifolds which are the total spaces of splitting bundles over projective spaces. We prove this conjecture in several special cases, and assuming the validity of our conjecture we check the integrality of genus one BPS numbers of local Calabi-Yau 5-folds defined by A. Klemm and R. Pandharipande.

References in corpus (3)

• Enumerative geometry of Calabi-Yau 4-folds
• Topological Strings and (Almost) Modular Forms
• Two-Point Gromov-Witten Formulas for Symplectic Toric Manifolds

Cited by in corpus (1)

• Localized standard versus reduced formula and genus one local Gromov-Witten invariants