Gauss-Manin connection associated to the versal deformation of the singularity \(A_\mu\) and zeros of the hyperelliptic integral

DOI10.1016/S0007-4497(01)01103-4zbMath1064.32023OpenAlexW1998773293MaRDI QIDQ1599933

Susumu Tanabé

Publication date: 26 June 2002

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0007-4497(01)01103-4

zbMATH Keywords

Abelian integralisomonodromic deformationGauss-Manin connectionPicard-Fuchs system

Mathematics Subject Classification ID

Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) (32S40) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Moduli and deformations for ordinary differential equations (e.g., Knizhnik-Zamolodchikov equation) (32G34)

Cites Work

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• Period mapping associated to a primitive form
• The complex exponent of a singularity does not change along strata mu=const
• Petrov modules and zeros of abelian integrals
• Monodromy of isolated singularities of hypersurfaces
• An explicit bound for the multiplicity of zeros of generic Abelian integrals
• Complete Abelian integrals as rational envelopes
• Formules de Picard-Lefschetz généralisées et ramification des intégrales

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