An Optimal Support Function related to the strong openness conjecture

TL;DR

This paper introduces an optimal support function for weighted L^2 integrals on superlevel sets of plurisubharmonic weights, providing a new proof of the strong openness conjecture for multiplier ideal sheaves.

Contribution

It presents a novel optimal support function that leads to a proof of the strong openness property of multiplier ideal sheaves.

Findings

Established an optimal support function for weighted L^2 integrals.

Proved the strong openness property of multiplier ideal sheaves.

Provided new insights into the structure of plurisubharmonic weights.

Abstract

In the present article, we obtain an optimal support function of weighted $L^2$ integrations on superlevel sets of psh weights, which implies the strong openness property of multiplier ideal sheaves.