Mixed Frobenius Structure and Local Quantum Cohomology
arXiv:1405.7476
Abstract
This paper is a sequel to arXiv:1209.5550 where the notion of mixed Frobenius structure (MFS) was introduced 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 non-equivariant limit of the quantum product twisted by a concave vector bundle. We show that such a MFS is naturally obtained as the non-equivariant limit of the Frobenius structure in the equivariant setting.
18 pages, v4. title changed from "Local Quantum Cohomology and Mixed Frobenius Structure". Introduction and section 5 are revised (though results unchanged). To appear in Publications of RIMS