Moduli space of rank three logarithmic connections on the projective line with three poles

2023/11/16 by Takafumi Matsumoto, Matsumoto, Takafumi · 2 citations
Mathematics · #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2311.10071

Abstract

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 ϕ-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.

Cited by

• Realization of symmetry of A^(1)*₂-surfaces as transformations of logarithmic connections
• Monodromy Representations: Decomposing Rank-Three Bundles over the Projective Line with Three Marked Points

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