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

• DOI: 10.48550/arxiv.1305.4397
• Publication Date: 2013-01-01
• Authors: Junyan Cao
• Keywords: Manifold (fluid mechanics); Kähler manifold; Filtration (mathematics); Characterization

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