Morphisms between Grassmannians, II

Abstract

Denote by $\mathbb{G}(k,n)$ the Grassmannian of linear subspaces of dimension $k$ in ${\mathbb{P}}^n$. We show that, if $\phi :\mathbb{G}(l,n)\to \mathbb{G}(k,n)$ is a non constant morphism and $l\ne 0,n-1$ then $l=k$ or $l=n-k-1$ and $\phi$ is an isomorphism.

References in corpus (1)

• Maximal disjoint Schubert cycles in rational homogeneous varieties