Generalization of Kodaira’s Embedding Theorem for Compact Kähler Manifolds with Semi-Positive Chern Class

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DOI: https://doi.org/10.28924/2291-8639-23-2025-72
Published: Mar 17, 2025
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Sayed Saber, Abdullah A. Alahmari, Generalization of Kodaira’s Embedding Theorem for Compact Kähler Manifolds with Semi-Positive Chern Class, Int. J. Anal. Appl., 23 (2025), 72.

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Sayed Saber, Abdullah A. Alahmari

Abstract

Kodaira embedding theorem states that a compact complex manifold can only be embedded into a complex projective space PN for some N if it admits a positive line bundle. Based on Chow’s theorem, projective algebraic manifolds are algebraic. The purpose of this study is to generalize Kodaira’s known theorem. We show that if X is a compact Kähler manifold of complex dimension n and its first Chern class is semi-positive and of rank n−1 at one point of X, then X can be embedded into PN for some integer N. Furthermore, we prove that this embedding is unique up to biholomorphism. We also show that X admits a Kähler metric whose Ricci curvature is bounded from below.

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