Curvature of Vector Bundles Associated to Holomorphic Fibrations

@inproceedings{Berndtsson2005CurvatureOV,
  title={Curvature of Vector Bundles Associated to Holomorphic Fibrations},
  author={Bo Berndtsson},
  year={2005}
}
  • Bo Berndtsson
  • Published 2005
Let L be a (semi)-positive line bundle over a Kähler man-ifold, X, fibered over a complex manifold Y. Assuming the fibers are compact and non-singular we prove that the hermitian vector bundle E over Y whose fibers over points y are the spaces of global sections over X y to L ⊗ K X/Y endowed with the L 2-metric is (semi)-positive in the sense of Nakano. As an application we prove a partial result on a conjecture of Griffiths on the positivity of ample bundles. This is a revised and much… CONTINUE READING
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