Curvature semipositivity of relative pluricanonical systems

Abstract

We prove semipositivity of the curvature of the Narashimhan-Simha metric on an arbitrary flat projective family of varieties with only canonical singularities. This also implies that the direct image of pluricanonical systems have a natural continuous hermitian strucutre with semipositive curvature curvature current in the sense of Nakano. This is an improvement of the author's preprint ``Refined semipositivity and moduli of canonical models (2005)''.

24pages no figure, Reference up dated and correction on the proof of Theorem 5.5

References in corpus (4)

• Invariance of Plurigenera
• Pseudo-effective line bundles on compact Kähler manifolds
• Curvature of vector bundles associated to holomorphic fibrations
• Variation of Bergman kernels of adjoint line bundles

Cited by in corpus (3)

• Canonical singular hermitian metrics on relative logcanonical bundles
• Bergman kernels and the pseudoeffectivity of relative canonical bundles
• Boundary asymptotics of the relative Bergman kernel metric for curves