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arXiv · 1305.4397

A remark on compact K\"ahler manifolds with nef anticanonical bundles and its applications

Junyan Cao
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Abstract

Let $(X, \omega_X)$ be a compact K\"ahler manifold such that the anticanonical bundle $-K_X$ is nef. We prove that the slopes of the Harder-Narasimhan filtration of the tangent bundle with respect to a polarization of the form $\omega_X^{n-1}$ are semi-positive. As an application, we give a characterization of rationally connected compact K\"ahler manifolds with nef anticanonical bundles. As another application, we give a simple proof of the surjectivity of the Albanese map.

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Junyan Cao. 2013-05-19. A remark on compact K\"ahler manifolds with nef anticanonical bundles and its applications. https://arxiv.org/abs/1305.4397

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