On the coherence of the L 2 subsheaf for a singular Hermitian metric whose determinant has analytic singularities

Key Points

• The research aims to investigate the coherence of the L2 subsheaf associated with a specific class of singular Hermitian metrics.
• Analyzed locally square integrable holomorphic sections
• Examined vector bundles with semi-positive curved singular Hermitian metrics
• Studied the induced determinant metrics for singularities
• Confirmed coherence of the L2 subsheaf
• Identified analytic singularities within the determinant metric
• Demonstrated implications for understanding vector bundles with singular Hermitian metrics