  The leading classical asymptotics of Virasoro conformal blocks on the Riemann
sphere with n generic and n-3 "heavy" degenerate field insertions can be
described in terms of the geometry of Garnier system describing the monodromy
preserving deformations of second order Fuchsian differential equations on an
n-punctured sphere. This allows us to characterise the leading classical
asymptotics of Virasoro conformal blocks completely, and to clarify in which
sense conformal field theory represents a quantisation of the isomonodromic
deformation problem.
