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

2022/05/09 by Vishnyakova, Elizaveta, Borovoi, Mikhail · 2 citations
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2205.04380

Abstract

Any complex-analytic vector bundle \mathbb E admits naturally defined homotheties ϕ_α, α∈ \mathbb 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 \mathbb 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.

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