Conjecture 𝒪 for Projective Complete Intersections

Source abstract

Abstract Conjecture ${{\mathcal{O}}}$ and Gamma conjectures for quantum cohomology of Fano manifolds were proposed by Galkin, Golyshev, and Iritani [ 16]. We prove Conjecture ${{\mathcal{O}}}$ for Fano complete intersections in projective spaces. The main tools to compute relevant genus-zero Gromov–Witten invariants with primitive insertions are the genus-one topological recursion relation and Zinger’s standard-versus-reduced formula. We also prove a related conjecture of Galkin [ 15] for projective Fano complete intersections.