Curvature of vector bundles associated to holomorphic fibrations

• 成果类型: Article
• 署名作者: Berndtsson, Bo
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2009.169.531
• 发表日期: 2009
• 页码: 531-560
• 关键词: projective embeddings; pseudoconvex domains; scalar curvature; monge-ampere; fiber spaces; SURFACES; operator; equation; CURVES

摘要

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 nonsingular 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 circle times K-X/Y, endowed with the L-2-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.