Positivity and vanishing theorems for ample vector bundles

By Kefeng Liu, Xiaofeng Sun, Xiaokui Yang. 2010

61 citations recorded by the source corpus.

In this paper, we study the Nakano-positivity and dual-Nakano-positivity of certain adjoint vector bundles associated to ample vector bundles. As applications, we get new vanishing theorems about ample vector bundles. For example, we prove that if $E$ is an ample vector bundle over a compact K\"ahler manifold $X$, $S^kE\ts \det E$ is both Nakano-positive and dual-Nakano-positive for any $k\geq 0$. Moreover, $H^{n,q}(X,S^kE\ts \det E)=H^{q,n}(X,S^kE\ts \det E)=0$ for any $q\geq 1$. In particular, if $(E,h)$ is a Griffiths-positive vector bundle, the naturally induced Hermitian vector bundle $(S^kE\ts \det E, S^kh\ts \det h)$ is both Nakano-positive and dual-Nakano-positive for any $k\geq 0$.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/2d8fcca6c364bb0ef3322487078b10cb0234dc30

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In Applied Mathematics

1. Xiaokui Yang
2. Kefeng Liu
3. Valentino Tosatti
4. Fang Zheng
5. B. Weinkove
6. Lei Ni

In Geometry and Topology

1. Xiaokui Yang
2. Kefeng Liu
3. Valentino Tosatti
4. Fang Zheng
5. B. Weinkove
6. Lei Ni

Citations in the corpus

• Ricci Curvatures on Hermitian manifolds (2014, background): “In fact, as described in [39], there is a natural Hermitian metric g on L induced by the Hermitian metric ωh on E = T M .”