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

Abstract

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

34 pages, part of the author's PhD Thesis