A new two-parameter family of isomonodromic deformations over the five punctured sphere

Abstract : The object of this paper is to describe an explicit two--parameter family of logarithmic flat connections over the complex projective plane. These connections have dihedral monodromy and their polar locus is a prescribed quintic composed of a circle and three tangent lines. By restricting them to generic lines we get an algebraic family of isomonodromic deformations of the five--punctured sphere. This yields new algebraic solutions of a Garnier system. Finally, we use the associated Riccati one--forms to construct an interesting non--generic family of transversally projective Lotka--Volterra foliations.
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  • HAL Id : hal-01176199, version 3
  • ARXIV : 1507.02863

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Arnaud Girand. A new two-parameter family of isomonodromic deformations over the five punctured sphere. Bulletin de la société mathématique de France, 2016, 144 (2), pp.339-368. ⟨hal-01176199v3⟩

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