Susumu Tanabe, Kumamoto University
Mixed Hodge structure and period integrals of the affine complete intersection

We calculate the period integrals of a deformed affine complete intersection (CI) in an algebraic torus in the form of their Mellin transforms. Our main result establishes a relationship between the poles of Mellin transform of period integrals (that is responsible for the monodromy of them), the mixed Hodge structure on the cohomology of the hypersurface obtained by Cayley trick from the initial CI, the hypergeometric differential system of Horn type and the Euler characteristic of fibres (after the Khovansky formula). It is possible to calculate global monodromy of the HG system obtained by my method and to show that the consequences of homological mirror symmetry hold between generic Calabi-Yau CI variety and the CI of Givental' type.

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