Bergman kernels and subadjunction

Abstract

In this article our main result is a more complete version of the statements obtained in {\rm [6]}. One of the important technical point of our proof is an $L^{\frac{2}{m}}$ extension theorem of Ohsawa-Takegoshi type, which is derived from the original result by a simple fixed point method. Moreover, we show that these techniques combined with an appropriate form of the"invariance of plurigenera" can be used in order to obtain a new proof of the celebrated Y. Kawamata subadjunction theorem.

References in corpus (6)

• Hodge metrics and the curvature of higher direct images
• Extension of log pluricanonical forms from subvarieties
• Basic properties of log canonical centers
• Extension of twisted Hodge metrics for Kähler morphisms
• Semipositivity theorem for reducible algebraic fiber spaces
• Extension of sections via adjoint ideals

Cited by in corpus (8)

• New characterizations of plurisubharmonic functions and positivity of direct image sheaves
• Positivity of holomorphic vector bundles in terms of $L^p$-conditions of $\bar{\partial }$
• A solution of an $L^2$ extension problem with optimal estimate and applications
• Kodaira dimension of algebraic fiber spaces over abelian varieties
• On asymptotic base loci of relative anti-canonical divisors of algebraic fiber spaces
• On the hyperbolicity of base spaces for maximally variational families of smooth projective varieties
• Linear invariants of complex manifolds and their plurisubharmonic variations
• Pseudonorms on direct images of pluricanonical bundles