Virasoro Correlation Functions on Hyperelliptic Riemann Surfaces

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 ≥  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.