On Triple Veronese Embeddings of ₙ in the Grassmannians

الأصل · EN

We classify all the embeddings of Pₙ in a Grassmannian Gr(1,N) such that the composition with Plücker embedding is given by a linear system of cubics on Pₙ. As a corollary in the direction of the Hartshorne conjecture, we prove that every vector bundle giving such an embedding, splits if n≥ 3.