Singular Hermitian metrics with isolated singularities

TL;DR

This paper investigates the properties of singular Hermitian metrics with isolated singularities, focusing on the coherence of higher rank multiplier ideal sheaves using advanced analytical tools.

Contribution

It introduces a higher rank analogue of multiplier ideal sheaves and proves their coherence employing Hörmander's $L^2$ estimates and a singular Demailly--Skoda type result.

Findings

Established coherence of higher rank multiplier ideal sheaves.

Extended analytical techniques to singular Hermitian metrics.

Provided new tools for studying complex geometric structures.

Abstract

In this paper, we study the coherence of a higher rank analogue of a multiplier ideal sheaf. Key tools of the study are H\"ormander's $L^2$-estimate and a singular version of a Demailly--Skoda type result.