On manifolds of small degree

  • Paltin Ionescu

    Bucharest, Romania


Let be a complex connected projective, non-degenerate, linearly normal manifold of degree . The main result of this paper is a classification of such manifolds. As a by-product of the classification it follows that these manifolds are either rational or Fano. In particular, they are simply connected (hence regular) and of negative Kodaira dimension. Moreover, easy examples show that is the best possible bound for such properties to hold true. The proof of our theorem makes essential use of the adjunction mapping and, in particular, the main result of [15] plays a crucial role in the argument.

Cite this article

Paltin Ionescu, On manifolds of small degree. Comment. Math. Helv. 83 (2008), no. 4, pp. 927–940

DOI 10.4171/CMH/149