Mixed Frobenius Structure and Local Quantum Cohomology

Yukiko Konishi; Satoshi Minabe

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arXiv · 1405.7476

Mixed Frobenius Structure and Local Quantum Cohomology

Yukiko Konishi·Satoshi Minabe

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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.

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BibTeX RIS

Yukiko Konishi, Satoshi Minabe. 2015-09-19. Mixed Frobenius Structure and Local Quantum Cohomology. https://arxiv.org/abs/1405.7476

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