  $N$-point functions of holomorphic fields in conformal field theories can be
calculated by methods from algebraic geometry. We establish explicit formulas
for the 2-point function of the Virasoro field on hyperelliptic Riemann
surfaces of genus $g\geq 1$. Virasoro $N$-point functions for higher $N$ are
obtained inductively, and we show that they have a nice graph representation.
We discuss the 3-point function with application to the $(2,5)$ minimal model.
