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Nesting maps of Grassmannians

Corrado De ConciniZinovy Reichstein — 2004

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Let F be a field and G r i , F n be the Grassmannian of i -dimensional linear subspaces of F n . A map f : G r i , F n G r j , F n is called nesting if l f l for every l G r i , F n . Glover, Homer and Stong showed that there are no continuous nesting maps G r i , C n G r j , C n except for a few obvious ones. We prove a similar result for algebraic nesting maps G r i , F n G r j , F n , where F is an algebraically closed field of arbitrary characteristic. For i = 1 this yields a description of the algebraic sub-bundles of the tangent bundle to the projective space P F n .

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