Quasi-positive curvature and projectivity

Abstract:

In this paper, we first prove that a compact Kähler manifold is projective if it satisfies certain quasi-positive curvature conditions, including quasi-positive $S_2^\perp$, $S_2^+$, $\operatorname {Ric}_3^\perp$, $\operatorname {Ric}_3^+$ or $2$-quasi-positive $\operatorname {Ric}_k$. Subsequently, we prove that a compact Kähler manifold with a special holonomy group is projective if it satisfies some non-negative curvature condition, including non-negative $S_2^\perp$, $S_2^+$, $\operatorname {Ric}_3^\perp$, $\operatorname {Ric}_3^+$ or $2$-non-negative $\operatorname {Ric}_k$.