LINEAR-SYSTEMS ON PROJECTIVE SPACES

In the paper the properties ($) over tilde N-p (a generalization of the properties N-p for projectively normal embeddings of projective varieties) are investigated for noncomplete Veronese embeddings. It is shown that the linear projection of a complete Veronese embedding P-n--> P-N from a general linear subspace of P-N of low dimension satisfies property ($) over tilde N-0. Moreover, Theorem 3.1 yields an upper bound for p for a noncomplete Veronese embedding of the projective plane P-2 to satisfy property ($) over tilde N-p.