Bergman kernels and the pseudoeffectivity of relative canonical bundles

2008/10/20 by Bo Berndtsson, Mihai Păun · 26 citations
Mathematics · #Geometry and complex manifolds #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows

paper · doi:10.1215/00127094-2008-054

Abstract

The main result of this article is a (practically optimal) criterion 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 [40], [41] and F. Campana [6]. As a byproduct, we give a simple and direct proof of a recent result due to C. Hacon and J. McKernan [16] and S. Takayama [29], [30] concerning the extension of twisted pluricanonical forms. More applications will be offered in [4], the sequel to this article

Citations

• On the extension ofL 2 holomorphic functions

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Related

• Invariance for multiples of the twisted canonical bundle
• Variation of Bergman kernels of adjoint line bundles
• Twisted cotangent bundles of Hyperkähler manifolds
• Positivity of twisted relative pluricanonical bundles and their direct images
• Direct images of pseudoeffective cotangent bundles