  Widely spread cruel misconceptions and mistakes in the calculation of
multi-loop superstring amplitudes are exposed. Correct calculations are given.
It is shown that the cardinal mistake in the gauge fixing procedure presents ab
ovo in the Verlinde papers. The mistake was reproduced in following proposals
including the recent papers. The modular symmetry of the multi-loop superstring
amplitudes is clarified, an incorrectness of previous conjectures being shown.
It is shown that the Berezin-type integral versus boson and fermion moduli is
doubt under non-split transformations mixing fermion integration variables to
the boson integration ones. In particular, due to singularities in moduli of
the given spin structure, the integral can be finite or divergent dependently
on the integration variables employed. Hence, unlike naive expectations, the
multi-loop superstring amplitude is ambiguous. Nevertheless, the ambiguity is
totally resolved by the requirement to preserve local symmetries of the
superstring amplitude. In the Verlinde world-sheet description it includes,
among other thing, the requirement that the amplitude is independent of the
gravitino field locations. In action the resolution of the ambiguity in the
Verlinde scheme is achieved by going to the supercovariant gauge. As it has
been argued earlier, the resulted arbitrary-loop amplitudes are finite.
