On Triple Veronese Embeddings of $\PP_n$ in the Grassmannians

Details On Triple Veronese Embeddings of $\PP_n$ in the Grassmannians On Triple Veronese Embeddings of $\PP_n$ in the Grassmannians

2008-06-04

arxiv.org/abs/0806.0777v6

Mathematics

Algebraic Geometry

12 pages, many changes

Scientific paper

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 $n\geq 3$.

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