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Gauss-Manin connexions, logarithmic forms and hypergeometric functions. (English) Zbl 0888.32017

Berrick, A. J. (ed.) et al., Geometry from the Pacific Rim. Proceedings of the Pacific Rim geometry conference, National University of Singapore, Republic of Singapore, December 12–17, 1994. New York, NY: Walter de Gruyter. 1-21 (1997).
The Gauss-Manin connection associated to the simple isolated hypersurface singularities \(A_\mu\) (resp. complete intersections \(S_\mu)\) are studied, and solutions of the corresponding system of differential equations are given in terms of generalised hypergeometric functions. The approach of K. Hanoto and I. M. Gelfand to study integrals of type \(J(t)= \int F_0^{\lambda_0} (z,t)\) \(F^{\lambda_1} (z,t)dz\) where \(F_0\), \(F_1\) are quadratic or higher order polynomials with respect to \(z=(z_1, \dots, z_n)\) is used.
For the entire collection see [Zbl 0870.00032].

MSC:

32S30 Deformations of complex singularities; vanishing cycles
33C20 Generalized hypergeometric series, \({}_pF_q\)
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
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