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In this paper, we classify the algebraic isomonodromic deformations that canbe obtained through restriction to generic lines of logarithmic flatconnections on the complex projective plane $\mathbb{P}^2_\mathbb{C}$ whosesingular locus is a quintic curve. We then explicitly compute the (finite)finite mapping class group orbits of the associated points in the charactervariety and describe the new algebraic Garnier solutions that can be obtainedthrough this procedure.

Algebraic isomonodromic deformations of the five punctured sphere arising from quintic plane curves