Abstract

Denote by \({\mathbb {G}}(k,n)\) the Grassmannian of linear subspaces of dimension k in \({\mathbb {P}}^n\) . We show that if \(\varphi :{\mathbb {G}}(l,n) \rightarrow {\mathbb {G}}(k,n)\) is a nonconstant morphism and \(l \not =0,n-1\) , then \(l=k\) or \(l=n-k-1\) and \(\varphi \) is an isomorphism.

中文翻译：

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格拉斯曼主义者之间的态射，II

摘要

用\({\mathbb {G}}(k,n)\)表示\({\mathbb {P}}^n\)中k维线性子空间的格拉斯曼。我们证明，如果\(\varphi :{\mathbb {G}}(l,n) \rightarrow {\mathbb {G}}(k,n)\)是非常数态射且\(l \not =0， n-1\)，则\(l=k\)或\(l=nk-1\)和\(\varphi \)是同构。