Characterization of pseudo-effective vector bundles by singular Hermitian metrics

Masataka Iwai

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arXiv · 1804.02146

Characterization of pseudo-effective vector bundles by singular Hermitian metrics

Masataka Iwai

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Abstract

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 applications, 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.

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Masataka Iwai. 2021-03-16. Characterization of pseudo-effective vector bundles by singular Hermitian metrics. https://arxiv.org/abs/1804.02146

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