On embedded products of Grassmannians Original Research Article

Let Γ′ and Γ be two Grassmannians. The standard embedding φ:Γ′×Γ→P̄ is obtained by combining the Plücker and Segre embeddings. Given a further embedding η:Γ′×Γ′→P′, we find a sufficient condition for the existence of α\inAut(Γ) and of a collineation ψ:P̄→P′ such that η=(idΓ′×α)φψ.