Nadel–Nakano vanishing theorems of vector bundles with singular Hermitian metrics
Nadel–Nakano vanishing theorems of vector bundles with singular Hermitian metrics
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具有奇异 Hermitian 度量的向量丛的 Nadel–Nakano 消失定理
DOI：
10.5802/afst.1666
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
M. Iwai
中科院分区：
文献类型：
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作者：
M. Iwai
研究了向量丛的奇异厄米特度量。首先，我们证明了具有奇异厄米特度量的向量丛的局部平方可积全纯截面层在某些假设下是凝聚的，它是乘子理想层的高阶类比。其次，我们证明了具有奇异Hermitian度量的向量丛的Nadel-Nakano型消失定理。我们不使用奇异厄米度量的近似技术。我们将这些定理应用于由全纯截面和大向量丛诱导的奇异厄米特度量，得到了Griffiths消失定理的一个推广。最后，我们给出了Ohsawa消失定理的一个推广。
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.