Two-loop statsum of superstring

It is discussed, whether there is a choice of odd moduli on super-Riemnann surfaces of genus p ≥ 2, which leads to vanishing of statistical sums of of superstrings before integration over the space of even moduli. The answer is shown to be positive at least for p=2, when odd moduli are localized at ramification points. relation between various definitions of many-lopp statistical sums in superstring theory is discussed