Hodge metrics and the curvature of higher direct images

Christophe Mourougane (1) , Shigeharu Takayama (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Graduate School of Mathematical Sciences[Tokyo]

Using the harmonic theory developed by Takegoshi for representation of relative cohomology and the framework of computation of curvature of direct images bundles by Berndtsson, we prove that the higher direct images by a smooth morphism of the relative canonical bundle twisted by a semi-positive vector bundle are locally free and semi-positively curved, when endowed with a suitable Hodge type metric.

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

Christophe Mourougane, Shigeharu Takayama. Hodge metrics and the curvature of higher direct images. Annales Scientifiques de l'École Normale Supérieure, 2008, 41 (6), pp.905-924. ⟨hal-00164943v2⟩