Note on the singular Hermitian metrics with analytic singularities

TL;DR

This paper investigates the properties of sheaves of square integrable holomorphic sections of vector bundles with semi-positive singular Hermitian metrics, confirming coherence under certain analytic singularity conditions.

Contribution

It establishes the coherence of these sheaves when the determinant metric exhibits analytic singularities, advancing understanding of singular Hermitian metrics.

Findings

Confirmed coherence of sheaves with analytic singularities

Analyzed semi-positive curved singular Hermitian metrics

Extended the theory of singular Hermitian metrics

Abstract

We study the sheaf of locally square integrable holomorphic section of vector bundle with semi-positive curved singular Hermitian metric. We confirm the coherence when its induced determinant metric has analytic singularities.