(13001)Effective vanishing theorems for ample and globally generated vector bundles


By proving an integral formula of the curvature tensor of E⊗detE, we observe that the curvature of E⊗detE 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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