Quasi-positive curvature and projectivity

2024/11/07 by Y. J. Du, Du, Yiyang, Yanyan Niu +1
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2411.04621

openalex publication_date 2024/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 S₂^⊥, S₂⁺, Ric₃^⊥, Ric₃⁺ or 2-quasi-positive Ric_k. Subsequently, we prove that a compact Kähler manifold with a restricted holonomy group is both projective and rationally conected if it satisfies some non-negative curvature condition, including non-negative S₂^⊥, S₂⁺, Ric₃^⊥, Ric₃⁺ or 2-non-negative Ric_k.

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