Mixed Frobenius Structure and Local Quantum Cohomology

Abstract

In a previous paper, the authors introduced the notion of mixed Frobenius structure (MFS) as a generalization of the structure of a Frobenius manifold. Roughly speaking, the MFS is defined by replacing a metric of the Frobenius manifold with a filtration on the tangent bundle equipped with metrics on its graded quotients. The purpose of the current paper is to construct a MFS on the cohomology of a smooth projective variety whose multiplication is the nonequivariant limit of the quantum product twisted by a concave vector bundle. We show that such a MFS is naturally obtained as the nonequivariant limit of the Frobenius structure in the equivariant setting.