A global approximation result by Al Taylor and the strong openness conjecture in C^n

TL;DR

This paper enhances a global approximation theorem for holomorphic functions in weighted Hilbert spaces in C^n, utilizing Hörmander's L^2-estimates and solving the strong openness conjecture, while also providing a counterexample to a related conjecture.

Contribution

It improves Al Taylor's approximation result in C^n and addresses the strong openness conjecture, including a counterexample to a global version.

Findings

Improved approximation theorem for holomorphic functions in weighted spaces

Solution of the strong openness conjecture in C^n

Counterexample to a global strong openness conjecture

Abstract

We improve a global approximation result by Al Taylor in C^n for holomorphic functions in weighted Hilbert spaces. The main tools are a variation of the theorem of Hormander on weighted L^2-estimates for the dbar-equation together with the solution of the strong openness conjecture. A counterexample to a global strong openness conjecture in Cn is also given here.