The Schlesinger equations are a system of differential equations for n + 2 matrix-valued functions A i : C n + 2 → → M a t ( m , C ) , given by ∂ ∂ A i ∂ ∂ λ λ j = [ A i , A j ] λ λ i − − λ λ j j ≠ ≠ i ∑ ∑ j ∂ ∂ A i ∂ ∂ λ λ j = 0.