Speaker
Description
In the early 1980-ies I. Skornyakov and I proved that a two-sided complex supergrassmannian is not superprojective.
This demonstrated that the role of supergrassmannians in algebraic supergeometry cannot be the same as the role of grassmannians in algebraic geometry. In particular, it motivated the sudy of embeddings of one supergrassmannian into another supergrassmannian.This study has been delayed for 40 years, and in this talk I will explain if and how one supergrassmannian can be embedded into another supergrassmannian so that the pullback of the Berezinian canonical sheaf from the larger supergrassmannian is isomorphic to the canonical sheaf of the smaller supergrassmannian. I call such embeddings linear and will outline a classification of linear embedddings of (possibly isotropic) supergrassmannians into other (possibly isotropic) supergrassmannians. A possible application is a classification of linear ind-supergrassmannians. The Sato supergrassmannian is a linear supergrassmannian.
