{"paper":{"title":"On embeddings of the Grassmannian $Gr(2,m)$ into the Grassmannian $Gr(2,n)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Minhyuk Kwon","submitted_at":"2016-09-22T05:51:37Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06827","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}