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Modules of the Abelian integrals and the Picard–Fuchs systems*

D Novikov

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Recommended by A I Neishtadt

We give a simple proof of an isomorphism between two Bbb C(t)-modules corresponding to bivariate polynomial H with non-degenerate highest homogeneous part: the module of relative cohomologies Λ2/dHwedgeΛ1 and the module of Abelian integrals. Using this isomorphism, we prove the existence and deduce some properties of the corresponding Picard–Fuchs system.


PACS

02.30.Hq Ordinary differential equations

02.40.-k Geometry, differential geometry, and topology

MSC

37A35 Entropy and other invariants, isomorphism, classification

34C08 Connections with real algebraic geometry (fewnomials, desingularization, zeros of Abelian integrals, etc.)

14K20 Analytic theory; abelian integrals and differentials

14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)

Subjects

Mathematical physics

Dates

Issue 5 (September 2002)

Received 16 October 2001, in final form 10 June 2002

Published 15 July 2002



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