Geodesic
Curvature of vector bundles associated to holomorphic fibrations
Bo Berndtsson1
1 Department of Mathematical Sciences<br/>Chalmers University of Technology and the University of Göteborg<br/>412 96 Göteborg<br/>Sweden
Annals of mathematics, Tome 169 (2009) no. 2, pp. 531-560.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 $X_y$ to $L\otimes K_{X/Y}$, 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.
DOI : 10.4007/annals.2009.169.531

Bo Berndtsson 1

1 Department of Mathematical Sciences<br/>Chalmers University of Technology and the University of Göteborg<br/>412 96 Göteborg<br/>Sweden 
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Bo Berndtsson. Curvature of vector bundles associated to holomorphic fibrations. Annals of mathematics, Tome 169 (2009) no. 2, pp. 531-560. doi : 10.4007/annals.2009.169.531. http://geodesic.mathdoc.fr/articles/10.4007/annals.2009.169.531/

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