[en] We show the analyticity with respect to the argument of T_zz (or T_zθ) and obtain an expression, which is equivalent to that of the fermionic Green function in the level of correlation functions, and the spin structure dependence of the fermionic determinant in the presence of fermionic zero modes. We also discuss the role of supermoduli, the relation between the path integral and the operator formalisms and anomaly cancellations in the one-loop (periodic-periodic) spin structure sector of the heterotic string. (orig.)