A positivity property of ample vector bundles

Christophe Mourougane (1) , Shigeharu Takayama (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 Graduate School of Mathematical Sciences[Tokyo]

Using Fujita-Griffiths method of computing metrics on Hodge bundles, we show that for every semi-ample vector bundle $E$ on a compact complex manifold, and every positive integer $k$, the vector bundle $S^kE\otimes\det E$ has a continuous metric with Griffiths semi-positive curvature. If $E$ is ample, the metric can be made smooth and Griffiths positive.

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

Christophe Mourougane, Shigeharu Takayama. A positivity property of ample vector bundles. 2005. ⟨hal-00004912v1⟩