A degeneration approach to Skoda's Division Theorem

TL;DR

This paper introduces a new degeneration-based proof of Skoda's Division Theorem, leveraging positivity of direct image bundles, and also simplifies and extends the proof of the L^2 extension theorem.

Contribution

It provides a novel degeneration approach to Skoda's Division Theorem and improves the proof of the L^2 extension theorem using similar techniques.

Findings

New proof of Skoda's Division Theorem via degeneration

Simplified proof of the L^2 extension theorem

Extended the applicability of positivity techniques in complex analysis

Abstract

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 $L^2$ 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 $L^2$ extension theorem given by Berndtsson and Lempert.