Automorphisms and real structures for a Π-symmetric super-Grassmannian.

Any complex-analytic vector bundle E admits naturally defined homotheties ϕ α , α ∈ C ⁎ , i.e. ϕ α is the multiplication of a local section by a complex number α. We investigate the question when such automorphisms can be lifted to a non-split supermanifold corresponding to E. Further, we compute the automorphism supergroup of a Π-symmetric super-Grassmannian Π Gr n , k , and, using Galois cohomology, we classify the real structures on Π Gr n , k and compute the corresponding supermanifolds of real points. [ABSTRACT FROM AUTHOR]