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

2016/09/22 by Kwon, Minhyuk
#14M15 #32M10 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1609.06827

Abstract

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.

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