The geometry of $Π$-invertible sheaves

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

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