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Quantum cohomology and periods. (Cohomologie quantique et période.) (English. French summary) Zbl 1300.14055
Motivated by Givental’s work on mirror symmetry for toric complete intersections, the author finds an explicit relationship between solutions to the quantum differential equation and the periods for toric orbifold mirror pairs. The author also gives a detailed study of the mirror isomorphism of variations of Hodge structure for a mirror pair of Calabi-Yau hypersurfaces and shows that the A-model and B-model periods are equal. Several interesting questions are raised in the last section.

MSC:
14N35 Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects)
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
14D07 Variation of Hodge structures (algebro-geometric aspects)
14J33 Mirror symmetry (algebro-geometric aspects)
32G20 Period matrices, variation of Hodge structure; degenerations
53D37 Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category
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