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Morphisms between Grassmannians. (English) Zbl 1504.14084

Summary: Denote by \(\mathbf{G}(k,n)\) the Grassmannian of linear subspaces of dimension \(k\) in \(\mathbf{P}^n\). We show that if \(n>m\) then every morphism \(\varphi :\mathbf{G}(k,n) \to \mathbf{G}(l,m)\) is constant.

MSC:

14M15 Grassmannians, Schubert varieties, flag manifolds
14J45 Fano varieties
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References:

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