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Picard-Fuchs equations for relative periods and Abel-Jacobi map for Calabi-Yau hypersurfaces. (English) Zbl 1253.14036
The authors aim to provide further development on the mathematical structures underlying inhomogeneous Picard-Fuchs equations and Abel-Jacobi maps.
More explicitly, they study the variation of relative cohomology for a pair consisting of a smooth projective hypersurface and an algebraic subvariety in it. Among other things, using the variation formalism, the authors prove that the relative periods of toric B-branes on Calabi-Yau hypersurface satisfy the enhanced GKZ hypergeometric system proposed in physics literature. The solution to the enhanced hypergeometric system is also provided.

14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
33C50 Orthogonal polynomials and functions in several variables expressible in terms of special functions in one variable
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
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