Del pezzo surfaces as hyperplane sections

摘要

Let L be a very ample line bundle on a n-dimensional complex projective manifold X. In this article we classify parir (X, L) as above with some smooth A∈∣L∣ being del Pezzo, i.e., with a smooth A∈∣L∣ such that -K_A=(n-2)H for some ample line bundle H on A. We assume that n≥3 since otherwise we are in the completely understood case when A is an elliptic curve