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Curvature of Vector Bundles Associated to Holomorphic Fibrations

Berndtsson, Bo

Annals of mathematics, 2009-03, Vol.169 (2), p.531-560

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Título:
Curvature of Vector Bundles Associated to Holomorphic Fibrations
Autor: Berndtsson, Bo
Assuntos: Algebra ; Algebraic geometry ; Algebraic topology ; Coefficients ; Coordinate systems ; Curvature ; Dot product of vectors ; Exact sciences and technology ; General mathematics ; General, history and biography ; Matematik ; Mathematical analysis ; Mathematical functions ; Mathematical manifolds ; Mathematical vectors ; Mathematics ; Riemann manifold ; Sciences and techniques of general use ; Several complex variables and analytic spaces ; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds ; Vector fields
É parte de: Annals of mathematics, 2009-03, Vol.169 (2), p.531-560
Descrição: Let L be a (semi)-positive line bundle over a Kähler 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 to $X_y \,to\,L \otimes \,K_{X/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.
Editor: Princeton, NJ: Princeton University Press
Idioma: Inglês

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