ON THE HOLOMORPHIC FACTORIZATION FOR SUPERCONFORMAL FIELDS

For a generic value of the central charge, we prove the holomorphic fa ctorization of partition functions for free superconformal fields whic h are defined on a compact Riemann surface without boundary. The parti tion functions are viewed as functionals of the Beltrami coefficients and their fermionic partners, which variables parametrize superconform al classes of metrics.