Bergman kernels and subadjunction

TL;DR

This paper advances the understanding of Bergman kernels and subadjunction by developing an $L^{2/m}$ extension theorem and applying it to provide a new proof of Kawamata's subadjunction theorem.

Contribution

It introduces a novel $L^{2/m}$ extension theorem of Ohsawa-Takegoshi type and applies it to give a new proof of Kawamata's subadjunction theorem.

Findings

Developed a fixed point method for $L^{2/m}$ extension theorem

Connected extension techniques with invariance of plurigenera

Provided a new proof of Kawamata's subadjunction theorem

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 $\displaystyle L^{2\over m}$ 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.