Darboux–Halphen–Ramanujan Vector Field on a Moduli of Calabi-Yau Manifolds

• Younes Nikdelan ^[1]
  1. [1] Instituto de Matemática Pura e Aplicada, IMPA (Brasil)
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 14, Nº 1, 2015, págs. 71-100
• Idioma: inglés
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• Resumen

  • In this paper we obtain an ordinary differential equation H from a Picard– Fuchs equation associated with a nowhere vanishing holomorphic n-form. We work on a moduli space T constructed from a Calabi–Yau n-fold W together with a basis of the middle complex de Rham cohomology of W. We verify the existence of a unique vector field H onT such that its composition with the Gauss–Manin connection satisfies certain properties. The ordinary differential equation given by H is a generalization of differential equations introduced by Darboux, Halphen and Ramanujan.