Topology of Complements of Hyperplane Arrangements and Isomonodromic Deformations of Fuchsian Systems

We consider families of systems of first-order linear differential equations on complex linear spaces that represent the Cherednik variant of the Knizhnik–Zamolodchikov equations. For these families of equations, we prove a rigidity property with respect to a certain class of isomonodromic deformations; i.e., we show the absence of nontrivial special isomonodromic deformations with a movable divisor of singularities.