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arXiv · 1507.02863

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

Arnaud Girand
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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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Arnaud Girand. 2015-07-10. A new two--parameter family of isomonodromic deformations over the five punctured sphere. https://arxiv.org/abs/1507.02863

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