abstract: Our study concerns isomonodromic deformations of logarithmic connections of arbitrary rank on the Riemann sphere. We will explain how we can translate the algebraicity of the universal isomonodromic deformation in terms of the monodromy representation r of the initial connection. Namely, (the conjugacy class of) r has finite orbit under the mapping class group of the punctured sphere if and only if the deformation is algebraizable. The main arguments are Riemann-Hilbert correspondence and a topological construction. A byproduct of this work is a tool to construct some regular flat connections on ruled varieties.