  We study embeddability of superschemes into $\Pi$-projective spaces and into
supergrassmannians $G(1|1,n|n)$. We give some criteria based on the relation
with ${\mathbb{A}}^{0|1}$-torsors and ${\mathbb{A}}^{0|1}$-fibrations. We also
prove the existence of nice quotients for free actions of ${\mathbb{A}}^{0|1}$
on superschemes.
