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

TL;DR

This paper classifies algebraic isomonodromic deformations derived from logarithmic flat connections on the complex projective plane with a quintic curve as the singular locus, and describes new algebraic Garnier solutions.

Contribution

It provides a classification of algebraic isomonodromic deformations from quintic plane curves and explicitly computes associated mapping class group orbits and Garnier solutions.

Findings

Classification of algebraic isomonodromic deformations

Explicit computation of mapping class group orbits

Description of new algebraic Garnier solutions

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 $\mathbb{P}^2_\mathbb{C}$ 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.