Effective vanishing theorems for ample and globally generated vector bundles
Effective vanishing theorems for ample and globally generated vector bundles
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充足且全局生成的向量束的有效消失定理
DOI：
10.4310/cag.2015.v23.n4.a3
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
Xiaokui Yang
中科院分区：
文献类型：
--
作者：
Kefeng Liu;Xiaokui Yang
通过证明$E\ts \det E$的曲率张量的一个积分公式，观察到$E\ts \det E$的曲率张量与线丛的曲率张量非常相似，从而得到向量丛的若干新的Kodaira-Akizuki-中野型消失定理.作为特例，我们用解析方法代替Leray-Borel-LePotier谱序列，得到了充要向量丛、Nef向量丛和整体生成向量丛的消失定理.
By proving an integral formula of the curvature tensor of $E\ts \det E$, we observe that the curvature tensor of $E\ts \det E$ is very similar to that of a line bundle and obtain certain new Kodaira-Akizuki-Nakano type vanishing theorems for vector bundles. As special cases, we deduce vanishing theorems for ample, nef and globally generated vector bundles by analytic method instead of the Leray-Borel-Le Potier spectral sequence.