On embeddings of the Grassmannian $Gr(2,m)$ into the Grassmannian $Gr(2,n)$

Minhyuk Kwon

Published 2016-09-22Version 1

In this paper, we consider holomorphic embeddings of $Gr(2,m)$ into $Gr(2,n)$. We can study such embeddings by finding all possible total Chern classes of the pull-back of the universal bundles under these embeddings. To do this, we use the relations between Chern classes of the universal bundles and Schubert cycles together with properties of complex vector bundles of rank $2$ on Grassmannians. Consequently, we find a condition on $m$ and $n$ for which any holomorphic embedding of $Gr(2,m)$ into $Gr(2,n)$ is linear.