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arXiv · 1303.3301

Effective vanishing theorems for ample and globally generated vector bundles

Kefeng Liu·Xiaokui Yang
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Abstract

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.

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Kefeng Liu, Xiaokui Yang. 2013-03-13. Effective vanishing theorems for ample and globally generated vector bundles. https://arxiv.org/abs/1303.3301

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