Numerical characterisation of quadrics

Thomas Dedieu (1) , Andreas Höring (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LJAD - Laboratoire Jean Alexandre Dieudonné

Let $X$ be a Fano manifold such that $-K_X \cdot C \geq \dim X$ for every rational curve $C \subset X$. We prove that $X$ is a projective space or a quadric.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Thomas Dedieu, Andreas Höring. Numerical characterisation of quadrics. Algebraic Geometry, 2017, 4 (1), pp.120-135. ⟨10.14231/AG-2017-006⟩. ⟨hal-01979015⟩