Mixed Frobenius Structure and Local Quantum Cohomology
Yukiko KonishiKyoto University, Japan
Satoshi MinabeTokyo Denki University, Japan
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.
Cite this article
Yukiko Konishi, Satoshi Minabe, Mixed Frobenius Structure and Local Quantum Cohomology. Publ. Res. Inst. Math. Sci. 52 (2016), no. 1, pp. 43–62DOI 10.4171/PRIMS/173