Quantum Cohomology and Periods
Copyright policy )Quantum Cohomology and Periods
In a previous paper, the author introduced an integral 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 of toric complete intersections and the periods (or oscillatory integrals) of their mirrors. We describe in detail the mirror isomorphism of variations of integral Hodge structure for a mirror pair of Calabi-Yau hypersurfaces (Batyrev’s mirror).
quantum cohomology, Variation of Hodge structures (algebro-geometric aspects), toric variety, mirror symmetry, \(K\)-theory, Period matrices, variation of Hodge structure; degenerations, period, Mathematics - Algebraic Geometry, Mirror symmetry (algebro-geometric aspects), oscillatory integral, Mathematics - Symplectic Geometry, Structure of families (Picard-Lefschetz, monodromy, etc.), GKZ system, FOS: Mathematics, gamma class, orbifold, Symplectic Geometry (math.SG), variation of Hodge structure, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), 14N35, 14D05, 14D07, 14J33, 32G20, 53D37, Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category, Algebraic Geometry (math.AG)
quantum cohomology, Variation of Hodge structures (algebro-geometric aspects), toric variety, mirror symmetry, \(K\)-theory, Period matrices, variation of Hodge structure; degenerations, period, Mathematics - Algebraic Geometry, Mirror symmetry (algebro-geometric aspects), oscillatory integral, Mathematics - Symplectic Geometry, Structure of families (Picard-Lefschetz, monodromy, etc.), GKZ system, FOS: Mathematics, gamma class, orbifold, Symplectic Geometry (math.SG), variation of Hodge structure, Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants (algebro-geometric aspects), 14N35, 14D05, 14D07, 14J33, 32G20, 53D37, Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category, Algebraic Geometry (math.AG)
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