On Multivariate Picard–Fuchs Systems and Equations

Alexander G. Aleksandrov ()
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Alexander G. Aleksandrov: Institute of Control Sciences, Russian Academy of Sciences, Profsoyuznaya Str. 65, GSP-7, 117997 Moscow, Russia

J, 2023, vol. 6, issue 3, 1-23

Abstract: In this paper, we studied the Picard–Fuchs systems and equations which appear in the theory of Gauss–Manin systems and connections associated with deformations of isolated singularities. Among other things, we describe some interesting properties of such systems and relationships between them. Then we show how to calculate the fundamental solutions to the Gauss–Manin system for A μ -singularities and to the corresponding generalized Legendre equations in terms of the multidimensional Horn’s hypergeometric functions. In conclusion, some important questions concerning basic properties of the local and global Picard–Fuchs systems of Pfaffian type, involving integrability conditions and commuting relations, are discussed in some detail.

Keywords: Gauss–Manin systems and connections; Legendre equation; versal integrals; period integrals; deformations; logarithmic differential forms; Horn’s hypergeometric functions; Picard–Fuchs systems; Fuchsian equations (search for similar items in EconPapers)
JEL-codes: I1 I10 I12 I13 I14 I18 I19 (search for similar items in EconPapers)
Date: 2023
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