  Multi-loop superstring amplitude are calculated in the convenient gauge where
Grassmann moduli are carried by the 2D gravitino field. Generally, instead of
the modular symmetry, the amplitudes hold the symmetry under modular
transformations added by relevant transformations of the 2D local
supersymmetry. If a number of loops is larger than 3, the integration measures
are not modular forms. In this case the expression for the amplitude contains
an integral over the bound of the fundamental region of the modular group.
