Mixed Frobenius structure and the local A-model

Abstract

We define the notion of mixed Frobenius structure (MFS) which is a generalization of the structure of a Frobenius manifold. We construct an MFS on the cohomology of weak Fano toric surfaces and that of the three-dimensional projective space using local Gromov–Witten invariants. This is an analogue of the Frobenius manifold associated to the quantum cohomology in the local Calabi–Yau setting.