THE COMPLEX STRUCTURE OF SUPERMODULI SPACE

The moduli space of all super Riemann surfaces of genus g > 1 is endow ed with the structure of a complex (holomorphic) superorbifold (discre te manifold quotient) of dimension (3g - 3\2g - 2). 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, a nd then using various passages to subspaces and quotients to reduce to the actual supermoduli space.