Characterization of projective spaces and $mathbb{P}^r $-bundles as ample divisors

Jie Liu (1, 2)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 IRMAR - Institut de Recherche Mathématique de Rennes

Let X be a projective manifold of dimension n. Suppose that TX contains an ample subsheaf. We show that X is isomorphic to \mathbb{P}^n. As an application, we derive the classification of projective manifolds containing a P r-bundle as an ample divisor by the recent work of D. Litt.

Mots clés: minimal rational curves; ample sheaf; ample divisor; foliation; projective space

Domaines: Géométrie algébrique [math.AG]

Jie Liu. Characterization of projective spaces and $mathbb{P}^r $-bundles as ample divisors. Nagoya Mathematical Journal, 2019, 233, pp.155-169. ⟨10.1017/nmj.2017.31⟩. ⟨hal-01408052⟩