Quasi-positive curvature and projectivity

Yiyang Du; Yanyan Niu

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arXiv · 2411.04621

Quasi-positive curvature and projectivity

Yiyang Du·Yanyan Niu

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Abstract

In this paper, we first prove that a compact K\"ahler manifold is projective if it satisfies certain quasi-positive curvature conditions, including quasi-positive $S_2^\perp,\, S_2^+,\,\mbox{Ric}_3^\perp, \,\mbox{Ric}_3^+$ or $2$-quasi-positive $\mbox{Ric}_k$. Subsequently, we prove that a compact K\"ahler manifold with a restricted holonomy group is both projective and rationally conected if it satisfies some non-negative curvature condition, including non-negative $S_2^\perp,\, S_2^+,\,\mbox{Ric}_3^\perp, \,\mbox{Ric}_3^+$ or $2$-non-negative $\mbox{Ric}_k$.

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Yiyang Du, Yanyan Niu. 2024-11-07. Quasi-positive curvature and projectivity. https://arxiv.org/abs/2411.04621

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