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

A Bergman kernel proof of the Kawamata subadjunction theorem