Partial algebraic solutions of isomonodromy equations on genus 2 curves (Q2017444)

The author considers a logarithmic connection over a curve of genus \(g\) with \(n\) poles and a family of ramified coverings depending algebraically on a parameter \(t\). This leads to the definition of a family of isomonodromic connections over the family of curves and provides a partial algebraic solution of the corresponding isomonodromic equation. In the case of rank \(2\) on curves of genus \(2\) this is done by adapting the Doran-Andreev-Kitaev method for Hurwitz families. The author classifies all cases where the connection is Zariski dense monodromy.