A degeneration approach to Skoda’s division theorem

We prove a Skoda-type division theorem via a degeneration argument. The proof is inspired by B. Berndtsson and L. Lempert’s approach to the \(L^2\) $L^2$ extension theorem and is based on positivity of direct image bundles. The same tools are then used to slightly simplify and extend the proof of the \(L^2\) $L^2$ extension theorem given by Berndtsson and Lempert.