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Pré-Publication, Document De Travail Année : 2013

A remark on compact Kähler manifolds with nef anticanonical bundles and its applications

Junyan Cao
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Résumé

Let $(X, \omega_X )$ be a compact Kähler 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 Kähler manifolds with nef anticanonical bundles. As another application, we give a simple proof of the surjectivity of the Albanese map.
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Dates et versions

hal-00823947 , version 1 (19-05-2013)

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Junyan Cao. A remark on compact Kähler manifolds with nef anticanonical bundles and its applications. 2013. ⟨hal-00823947⟩

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