arXiv subjects
Publications and source records attributed to Minhyuk Kwon.
We classify smooth Schubert varieties S_0 in a rational homogeneous manifold S associated to a short root, and show that they are rigid in the sense that any subvariety of S having the same homology class as S_0 is induced by the action of Aut_0(S), unless S_0 is linear.
In this {paper}, we consider holomorphic embeddings of $Gr(2,m)$ into $Gr(2,n)$. We study such embeddings by finding all possible total Chern classes of the pull-back of the universal bundles under these embeddings. Using the relations between Chern classes of the universal bundles and Schubert cycles, together with properties of holomorphic vector bundles of rank $2$ on complex Grassmannians, we find conditions on $m$ and $n$ for which any holomorphic embedding of $Gr(2,m)$ into $Gr(2,n)$ is linear.