A Bergman kernel proof of the Kawamata subadjunction theorem

TL;DR

This paper provides a new proof of Kawamata's subadjunction theorem using Bergman kernels, an $L^{2/m}$ extension theorem, and refined previous results, offering a novel analytic approach to a key algebraic geometry result.

Contribution

It introduces a Bergman kernel-based proof of Kawamata's subadjunction theorem and establishes a new $L^{2/m}$ extension theorem of Ohsawa-Takegoshi type.

Findings

New proof of Kawamata's subadjunction theorem

Development of a new $L^{2/m}$ extension theorem

Enhanced techniques using Bergman kernels

Abstract

The main purpose of the following article is to give a proof of Y. Kawamata's celebrated subadjunction theorem in the spirit of our previous work on Bergman kernels. We will use two main ingredients : an $\displaystyle L^{2\over m}$--extension theorem of Ohsawa-Takegoshi type (which is also a new result) and a more complete version of our former results.