Hodge Metrics and Positivity of Direct Images
نویسندگان
چکیده
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 SE ⊗ detE 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.
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