Noncomplete linear systems on abelian varieties

Let be a smooth projective variety. Every embedding is the linear projection of an embedding defined by a complete linear system. In this paper the geometry of such not necessarily complete embeddings is investigated in the special case of abelian varieites. To be more precise, the properties of complete embeddings are extended to arbitrary embeddings, and criteria for these properties to be satisfied are elaborated. These results are applied to abelian varieties. The main result is: Let be a general polarized abelian variety of type and , such that is even, and . The general subvector space of codimension satisfies the property .