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C. DeConcini, Z. Reichstein, * Nesting maps
of Grassmannians, * Rendiconti di Matematica
Accademia Nazionale dei Lincei, s. 9, v. 15 (2004), 109--118.

**Abstract:**
Let F be a field and i < j be integers
between 1 and n. A map of Grassmannians
f : Gr(i, F^n) --> Gr(j, F^n) is called nesting, if
l is contained in f(l) for every l in Gr(i, F^n).
We show that there are no continuous nesting maps
over C and no algebraic nesting maps over
any algebraically closed field F, except for a few
obvious ones. The continuous case is due to Stong
and Grover-Homer-Stong; the algebraic case in
characteristic zero can also be deduced from
their results. In this paper we give
new proofs that work in arbitrary characteristic.
As a corollary, we give a description
of the algebraic subbundles of the tangent
bundle to the projective space P^n over F.
Another application can be found in a
a
recent paper of George Bergman.

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