Let \mathfrak{g}𝔤
be a simply laced Lie algebra, \widehat{\mathfrak{g}}_1𝔤̂1
the corresponding affine Lie algebra at level one, and
\mathcal{W}(\mathfrak{g})𝒲(𝔤)
the corresponding Casimir W-algebra. We consider
\mathcal{W}(\mathfrak{g})𝒲(𝔤)-symmetric
conformal field theory on the Riemann sphere. To a number of
\mathcal{W}(\mathfrak{g})𝒲(𝔤)-primary
fields, we associate a Fuchsian differential system. We compute
correlation functions of \widehat{\mathfrak{g}}_1𝔤̂1-currents
in terms of solutions of that system, and construct the bundle where
these objects live. We argue that cycles on that bundle correspond to
parameters of the conformal blocks of the W-algebra, equivalently to
moduli of the Fuchsian system.