Communications in Analysis and Geometry

Volume 23 (2015)

Number 4

Effective vanishing theorems for ample and globally generated vector bundles

Pages: 797 – 818

DOI: http://dx.doi.org/10.4310/CAG.2015.v23.n4.a3

Authors

Kefeng Liu (Center of Mathematical Science, Zhejiang University, Hangzhou, China; and Department of Mathematics, University of California at Los Angeles)

Xiaokui Yang (Academy of Mathematics and Systems Science, The Chinese Academy of Sciences, Beijing, China)

Abstract

By proving an integral formula of the curvature tensor of $E \otimes \textrm{det} \; E$, we observe that the curvature of $E \otimes \textrm{det} \; E$ 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 new 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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