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A degeneration approach to Skoda’s division theorem

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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.

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Acknowledgements

I am grateful to Dror Varolin for bringing this topic to my attention, for many helpful discussions and a lot of encouragement. I also thank Bo Berndtsson, László Lempert, Christian Schnell, and Xu Wang for providing useful comments and suggestions. Finally, I thank the anonymous referees for their helpful observations.

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  1. Department of Mathematics, Stony Brook University, Stony Brook, NY, 11794-3651, USA

    Roberto Albesiano

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  1. Roberto Albesiano
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Albesiano, R. A degeneration approach to Skoda’s division theorem. Math. Z. 306, 34 (2024). https://doi.org/10.1007/s00209-024-03435-6

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