TL;DR
This paper explores the relationship between quantum cohomology, K-theory, and mirror symmetry for toric orbifolds and Calabi-Yau hypersurfaces, providing explicit links between quantum differential equations and mirror periods.
Contribution
It introduces a Z-structure in quantum cohomology compatible with mirror symmetry and explicitly relates quantum solutions to mirror periods for toric complete intersections.
Findings
Explicit relationship between quantum differential equations and mirror periods.
Detailed description of mirror isomorphism for Calabi-Yau hypersurfaces.
Compatibility of Z-structure with mirror symmetry for toric orbifolds.
Abstract
In a previous paper, the author introduced a Z-structure in quantum cohomology defined by the K-theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds. Applying the quantum Lefschetz principle to the previous results, we find an explicit relationship between solutions to the quantum differential equation for toric complete intersections and the periods (or oscillatory integrals) of their mirrors. We describe in detail the mirror isomorphism of variations of Z-Hodge structure for a mirror pair of Calabi-Yau hypersurfaces (Batyrev's mirror).
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