Modules of square integrable holomorphic germs

TL;DR

This paper provides a shorter proof of the strong openness conjecture for plurisubharmonic functions and extends it to singular hermitian metrics on vector bundles, advancing complex analysis and geometry.

Contribution

It offers a more concise proof of a key conjecture and generalizes the result to broader settings involving vector bundles with singular metrics.

Findings

Shorter proof of the strong openness conjecture.

Extension to singular hermitian metrics on vector bundles.

Broader applicability in complex geometry.

Abstract

This paper was inspired by Guan and Zhou's recent proof of the so-called strong openness conjecture for plurisubharmonic functions. We give a proof shorter than theirs and extend the result to possibly singular hermitian metrics on vector bundles.