Nesting maps of Grassmannians

De Concini, Corrado, and Reichstein, Zinovy. "Nesting maps of Grassmannians." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 15.2 (2004): 109-118. <http://eudml.org/doc/252343>.

@article{DeConcini2004,
abstract = {Let $F$ be a field and $Gr(i, F^\{n\})$ be the Grassmannian of $i$-dimensional linear subspaces of $F^\{n\}$. A map $f : Gr(i, F^\{n\}) \rightarrow Gr(j, F^\{n\})$ is called nesting if $l \subset f(l)$ for every $l \in Gr(i, F^\{n\})$. Glover, Homer and Stong showed that there are no continuous nesting maps $Gr(i, \mathbb\{C\}^\{n\}) \rightarrow Gr(j, \mathbb\{C\}^\{n\})$ except for a few obvious ones. We prove a similar result for algebraic nesting maps $Gr(i, F^\{n\}) \rightarrow Gr(j, F^\{n\})$, 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 $P_\{F\}^\{n\}$.},
author = {De Concini, Corrado, Reichstein, Zinovy},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Grassmannian; Vector bundle; Cohomology ring; Chern class; Tangent bundle; vector bundle; cohomology ring; tangent bundle},
language = {eng},
month = {6},
number = {2},
pages = {109-118},
publisher = {Accademia Nazionale dei Lincei},
title = {Nesting maps of Grassmannians},
url = {http://eudml.org/doc/252343},
volume = {15},
year = {2004},
}

TY - JOUR
AU - De Concini, Corrado
AU - Reichstein, Zinovy
TI - Nesting maps of Grassmannians
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 2004/6//
PB - Accademia Nazionale dei Lincei
VL - 15
IS - 2
SP - 109
EP - 118
AB - Let $F$ be a field and $Gr(i, F^{n})$ be the Grassmannian of $i$-dimensional linear subspaces of $F^{n}$. A map $f : Gr(i, F^{n}) \rightarrow Gr(j, F^{n})$ is called nesting if $l \subset f(l)$ for every $l \in Gr(i, F^{n})$. Glover, Homer and Stong showed that there are no continuous nesting maps $Gr(i, \mathbb{C}^{n}) \rightarrow Gr(j, \mathbb{C}^{n})$ except for a few obvious ones. We prove a similar result for algebraic nesting maps $Gr(i, F^{n}) \rightarrow Gr(j, F^{n})$, 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 $P_{F}^{n}$.
LA - eng
KW - Grassmannian; Vector bundle; Cohomology ring; Chern class; Tangent bundle; vector bundle; cohomology ring; tangent bundle
UR - http://eudml.org/doc/252343
ER -