The geometry of $\Pi$-invertible sheaves

Abstract

Using the fact that $\Pi$-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 $\Pi$-projective superspace ${\mathbb{P}}_{\Pi ,B}^n$ over affine $k$ superschemes $B$, $k$ an algebraically closed field. We characterize morphisms into ${\mathbb{P}}_{\Pi ,B}^n$ and give a new interpretation of the composition of $\Pi$-invertible sheaves in terms of the algebra of $\mathbb{D}$.

References in corpus (1)

• Super Morita Theory

Cited by in corpus (3)

• Supergeometry of $\Pi$-Projective Spaces
• Pluri-Canonical Models of Supersymmetric Curves
• Super Morita Theory