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arXiv · 2006.13884

Compact K\"ahler manifolds with quasi-positive second Chern-Ricci curvature

Xiaokui Yang
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Abstract

Let $X$ be a compact K\"ahler manifold. We prove that if $X$ admits a smooth Hermitian metric $\omega$ with quasi-positive second Chern-Ricci curvature $\mathrm{Ric}^{(2)}(\omega)$, then $X$ is projective and rationally connected. In particular, $X$ is simply connected.

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Xiaokui Yang. 2020-06-24. Compact K\"ahler manifolds with quasi-positive second Chern-Ricci curvature. https://arxiv.org/abs/2006.13884

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