Finite orbits of the pure braid group on the monodromy of the $2$-variable Garnier system
In this paper we show that the $SL_{2}(\mathbb C)$ character variety of the Riemann sphere $Σ_5$ with five boundary components is a $5$-parameter family of affine varieties of dimension $4$. We endow this family of affine varieties with an action of the braid group and classify exceptional finite orbits. This action represents the nonlinear monodromy of the $2$ variable Garnier system and finite orbits correspond to algebraic solutions.
math.CA↗