Hodge metrics and positivity of direct images

Abstract

Building on Fujita-Griffiths method of computing metrics on Hodge bundles, we show that the direct image of an adjoint semi-ample line bundle by a projective submersion has a continuous metric with Griffiths semi-positive curvature. This shows that for every holomorphic semi-ample vector bundle $E$ on a complex manifold, and every positive integer $k$, the vector bundle $S^{k}E\otimes \det E$ has a continuous metric with Griffiths semi-positive curvature. If $E$ is ample on a projective manifold, the metric can be made smooth and Griffiths positive.

revised and expanded version of "A positivity property of ample vector bundles"

References in corpus (2)

• Vanishing theorems for ample vector bundles
• Curvature of vector bundles and subharmonicity of Bergman kernels

Cited by in corpus (14)

• Hodge metrics and the curvature of higher direct images
• On semipositivity, injectivity and vanishing theorems
• Extension of twisted Hodge metrics for Kähler morphisms
• Hermitian-Yang-Mills approach to the conjecture of Griffiths on the positivity of ample vector bundles
• Notes on variation of Lefschetz star operator and $T$-Hodge theory
• Curvature of higher direct image sheaves and its application on negative-curvature criterion for the Weil-Petersson metric
• Positivity and vanishing theorems for ample vector bundles
• Griffiths extremality, interpolation of norms, and Kähler quantization
• Complex Finsler vector bundles with positive Kobayashi curvature
• Remarks on the extension of twisted Hodge metrics
• Effective vanishing theorems for ample and globally generated vector bundles
• Relative $\dbar$-complex and its curvature properties
• Manifolds Containing an Ample P^1-bundle
• Positively curved Finsler metrics on vector bundles II