Superstring vertex operators and scattering amplitudes on arbitrary Riemann surfaces

The construction of scattering amplitudes involving arbitrary bosonic mass level states is considered in both the closed superstring and in the heterotic string theories, at any order of perturbation. From massless particle scattering on a general Riemann surface, the super-covariant form of the vertex operators is derived via factorization. The super-covariant rules, including the normal ordering prescriptions, to be used in computing amplitudes, are automatically given by this procedure. (orig.)