The geometry of Î -invertible sheaves

Using the fact that Π-invertible sheaves can be interpreted as locally free sheaves of modules for the super skew field D, we give a new construction of the Π-projective superspace PΠ,Bn over affine k superschemes B, k an algebraically closed field. We characterize morphisms into PΠ,Bn and give a new interpretation of the composition of Π-invertible sheaves in terms of the algebra of D.