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Regular singular holonomic systems of differential equations with given integrals. (English) Zbl 1118.35016

Summary: We develop an approach to the study of holonomic systems of differential equations with regular singularities along hypersurfaces. In particular, we investigate Picard-Fuchs systems satisfied by the elliptic, hyperelliptic and versal integrals, describe the corresponding minimal equations and analyze properties of their solutions.

MSC:

35N10 Overdetermined systems of PDEs with variable coefficients
35F05 Linear first-order PDEs
32S30 Deformations of complex singularities; vanishing cycles
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
35A20 Analyticity in context of PDEs
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