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

Sukmoon Huh

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

Algebraic Geometry 2010-03-04 v6

Authors: Sukmoon Huh

Abstract

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 $n\geq 3$ .

Keywords

triple Veronese embedding Grassmannians Plücker embedding linear system of cubics Hartshorne conjecture vector bundles splitting criterion

Cite

@article{arxiv.0806.0777,
  title  = {On Triple Veronese Embeddings of $\PP_n$ in the Grassmannians},
  author = {Sukmoon Huh},
  journal= {arXiv preprint arXiv:0806.0777},
  year   = {2010}
}

Comments

12 pages, many changes

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