Quantum Cohomology and Periods

Details Quantum Cohomology and Periods Quantum Cohomology and Periods

2011-01-24

arxiv.org/abs/1101.4512v3

Mathematics

Algebraic Geometry

39 pages, v2: improved the explanation on multi-generation, quintic example added, v3: one of the main theorem (Theorem 6.9) i

Scientific paper

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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