Nadel-Nakano vanishing theorems of vector bundles with singular Hermitian metrics

Masataka Iwai

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arXiv · 1802.01794

Nadel-Nakano vanishing theorems of vector bundles with singular Hermitian metrics

Masataka Iwai

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Abstract

We study a singular Hermitian metric of a vector bundle. First, we prove the sheaf of locally square integrable holomorphic sections of a vector bundle with a singular Hermitian metric, which is a higher rank analogy of a multiplier ideal sheaf, is coherent under some assumptions. Second, we prove a Nadel-Nakano type vanishing theorem of a vector bundle with a singular Hermitian metric. We do not use an approximation technique of a singular Hermitian metric. We apply these theorems to a singular Hermitian metric induced by holomorphic sections and a big vector bundle, and we obtain a generalization of Griffiths' vanishing theorem. Finally, we show a generalization of Ohsawa's vanishing theorem.

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BibTeX RIS

Masataka Iwai. 2018-02-06. Nadel-Nakano vanishing theorems of vector bundles with singular Hermitian metrics. https://arxiv.org/abs/1802.01794

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