$${\mathbb A}^{0|1}$$-Torsors, Quotients by Free $${\mathbb A}^{0|1}$$-Actions, and Embeddings into $$\Pi $$-Projective Spaces and Super-Grassmannians G(1|1, n|n)

We study embeddability of superschemes into Π-projective spaces and into supergrassmannians G(1∣1, n∣n). We give some criteria based on the relation with A-torsors and A -fibrations. We also prove the existence of nice quotients for free actions of A on superschemes.