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A family of flat connections on the projective space having dihedral monodromy and algebraic Garnier solutions
Arata Komyo1
1 Center for Mathematical and Data Sciences, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 30 (2021) no. 3, pp. 479-501.

A. Girand has constructed an explicit two-parameter family of flat connections over the complex projective plane ℙ 2 . These connections have dihedral monodromy and their polar locus is a prescribed quintic composed of a conic and three tangent lines. In this paper, we give a generalization of this construction. That is, we construct an explicit n-parameter family of flat connections over the complex projective space ℙ n . Moreover, we discuss the relation between these connections and the Garnier system.

A. Girand a construit une famille explicite de connexions à deux paramètres sur le plan projectif complexe ℙ 2 . Ces connexions ont une monodromie diédrale et leur lieu polaire est une quintique prescrite composée d’une conique et de trois droites tangentes. Dans cet article, nous donnons une généralisation de cette construction. Autrement dit, nous construisons une famille de connexions plates explicite à n paramètres sur l’espace projectif complexe ℙ n . De plus, nous discutons de la relation entre ces connexions et le système Garnier.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1682
Classification: 14H05, 14F35, 34M55
Keywords: algebraic function, Garnier system, isomonodromic deformation.

Arata Komyo 1

1 Center for Mathematical and Data Sciences, Kobe University, 1-1 Rokkodai-cho, Nada-ku, Kobe, 657-8501, Japan
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     title = {A family of flat connections on the projective space having dihedral monodromy and algebraic {Garnier} solutions},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
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Arata Komyo. A family of flat connections on the projective space having dihedral monodromy and algebraic Garnier solutions. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 30 (2021) no. 3, pp. 479-501. doi : 10.5802/afst.1682. https://afst.centre-mersenne.org/articles/10.5802/afst.1682/

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