2005/11/30 by Bo Berndtsson
Mathematics · #math.CV #math.AG #msc:32L15 #msc:32W05
published as Ann of Math (2) 169 (2009), no 2, pp 531-560 · This revision simplifies some proofs. An incorrect proof from the appendix has also been withdrawn (it was not used in the rest of the paper)
arxiv created 2007/08/20 · arxiv updated 2012/10/30
Let L be a (semi)-positive line bundle over a Kahler manifold, 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 Xy to L\gr KX/Y endowed with the L2-metric is (semi)-positive in the sense of Nakano. We also discuss various applications, among them a partial result on a conjecture of Griffiths on the positivity of ample bundles. This is a revised and much expanded version of a previous preprint with the title `` Bergman kernels and the curvature of vector bundles''.