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Calculation of Mixed Hodge Structures, Gauss-Manin Connections and Picard-Fuchs Equations

  • Hossein Movasati
Conference paper
Part of the Trends in Mathematics book series (TM)

Abstract

In this article we introduce algorithms which compute iterations of Gauss-Manin connections, Picard-Fuchs equations of Abelian integrals and mixed Hodge structure of affine varieties of dimension n in terms of differential forms. In the case n = 1 such computations have many applications in differential equations and counting their limit cycles. For n > 3, these computations give us an explicit definition of Hodge cycles.

Keywords

Mixed Hodge structure of affine varieties Gauss-Manin connection 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Hossein Movasati
    • 1
  1. 1.IMPA — Instituto de Matematica Pura e AplicadaJardim Botanico, Rio de Janeiro — RJBrazil

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