In this paper, we give complex geometric descriptions of the notions of algebraic geometric positivity of vector bundles and torsion-free coherent sheaves, such as nef, big, pseudo-effective, and weakly positive, by using singular hermitian metrics. As an application, we obtain a generalization of Mori’s result. We also give a characterization of the augmented base locus by using singular hermitian metrics on vector bundles and the Lelong numbers.
"Characterization of Pseudo-Effective Vector Bundles by Singular Hermitian Metrics." Michigan Math. J. Advance Publication 1 - 21, 2021. https://doi.org/10.1307/mmj/20195833