The complex structure of supermoduli space

The moduli space of all super Riemann surfaces of genus g>1 is endowed with the structure of a complex (holomorphic) superorbifold (discrete manifold quotient) of dimension . After the various problems in doing this have been discussed, the method adopted is that of defining the natural almost complex structure on the space of all `super almost complex structures' of genus g, proving it integrable, and then using various passages to subspaces and quotients to reduce to the actual supermoduli space.