Big vector bundles and compact complex manifolds with semi-positive tangent bundles

Xiaokui Yang

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arXiv · 1412.5156

Big vector bundles and compact complex manifolds with semi-positive tangent bundles

Xiaokui Yang

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Abstract

We classify compact K\"ahler manifolds with semi-positive holomorphic bisectional and big tangent bundles. We also classify compact complex surfaces with semi-positive tangent bundles and compact complex $3$-folds of the form $P(T^*X)$ whose tangent bundles are nef. Moreover, we show that if $X$ is a Fano manifold such that $P(T^*X)$ has nef tangent bundle, then $X\cong P^n$.

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Xiaokui Yang. 2014-12-16. Big vector bundles and compact complex manifolds with semi-positive tangent bundles. https://arxiv.org/abs/1412.5156

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