Bergman kernels and the pseudoeffectivity of relative canonical bundles

Abstract

The main result of the present article is a (practically optimal) criterium for the pseudoeffectivity of the twisted relative canonical bundles of surjective projective maps. Our theorem has several applications in algebraic geometry; to start with, we obtain the natural analytic generalization of some semipositivity results due to E. Viehweg and F. Campana. As a byproduct, we give a simple and direct proof of a recent result due to C. Hacon--J. McKernan, S. Takayama and H. Tsuji concerning the extension of twisted pluricanonical forms. More applications will be offered in the sequel of this article.

This is the third revision

References in corpus (1)

• Curvature semipositivity of relative pluricanonical systems

Cited by in corpus (7)

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• Bergman kernels and subadjunction
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• Relative adjoint transcendental classes and Albanese maps of compact Kaehler manifolds with nef Ricci curvature
• Extension of twisted Hodge metrics for Kähler morphisms
• On the extension of twisted holomorphic sections of singular hermitian line bundles
• Remarks on the extension of twisted Hodge metrics