On the generalized Teichmüller spaces and differential equations

It is well known that for the family F of Riemann surfaces {R(z)} defined by the equations y2 = x(x — l)(x — z), zεC — {0,1}, we have one independent abelian differential ω = y−1dx on each R(z) and if we consider z as a parameter on C — {0,1}, the integrals are solutions of the Gauss’s differential equation