%0 Journal Article
%T On Triple Veronese Embeddings of $\PP_n$ in the Grassmannians
%A Sukmoon Huh
%J Mathematics
%D 2008
%I arXiv
%X We classify all the embeddings of $\mathbb{P}_n$ in a Grassmannian $Gr(1,N)$ such that the composition with Pl\"{u}cker embedding is given by a linear system of cubics on $\mathbb{P}_n$. As a corollary in the direction of the Hartshorne conjecture, we prove that every vector bundle giving such an embedding, splits if $n\geq 3$.
%U http://arxiv.org/abs/0806.0777v6