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Moduli space of rank three logarithmic connections on the projective line with three poles
Takafumi Matsumoto1
1 Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8512, Japan
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 34 (2025) no. 3, pp. 657-730.

In this paper, we describe the moduli space of rank three parabolic logarithmic connections on the projective line with three poles for any local exponents. In particular, we show that the family of moduli spaces of rank three parabolic $\phi $-connections on the projective line with three poles is isomorphic to the family of $A^{(1)*}_2$-surfaces in Sakai’s classification of Painlevé equations. Through this description, we investigate the relation between the apparent singularities and underlying parabolic bundles.

Dans cet article, nous décrivons l’espace de modules des connexions logarithmiques paraboliques de rang trois sur la droite projective avec trois pôles pour des exposants locaux quelconques. En particulier, nous montrons que la famille des espaces de modules des $\phi $-connexions paraboliques de rang trois sur la droite projective à trois pôles est isomorphe à la famille des $A_2^{(1)*}$-surfaces dans la classification de Sakai des équations de Painlevé. Grâce à cette description, nous étudions la relation entre les singularités apparentes et les faisceaux paraboliques sous-jacents.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1821

Takafumi Matsumoto 1

1 Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8512, Japan
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Takafumi Matsumoto. Moduli space of rank three logarithmic connections on the projective line with three poles. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 34 (2025) no. 3, pp. 657-730. doi : 10.5802/afst.1821. https://afst.centre-mersenne.org/articles/10.5802/afst.1821/

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