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Positivity and the
Kodaira embedding theorem
Lei Ni and Fangyang Zheng |
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Geometry & Topology 26 (2022) 2491–2505
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DOI: 10.2140/gt.2022.26.2491
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Abstract |
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The Kodaira embedding theorem provides an effective characterization of projectivity of a Kähler manifold in terms the second cohomology. X Yang (2018) proved that any compact Kähler manifold with positive holomorphic sectional curvature must be projective. This gives a metric criterion of the projectivity in terms of its curvature. We prove that any compact Kähler manifold with positive scalar curvature (which is the average of holomorphic sectional curvature over –dimensional subspaces of the tangent space) must be projective. In view of generic –tori being nonabelian, this new curvature characterization is sharp in certain sense. |
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Keywords
Kähler manifolds, projective embedding, compact complex
manifolds, Kähler metrics, positive holomorphic sectional
curvature, $k^{\text{th}}$ scalar curvature
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Mathematical Subject Classification 2010
Primary: 53C55
Secondary: 53C44
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References |
Publication
Received: 21 January 2020
Revised: 13 April 2021
Accepted: 8 June 2021
Published: 13 December 2022
Proposed: Simon Donaldson
Seconded: Gang Tian, Tobias H Colding
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Authors |
| Lei Ni | |
| Department of Mathematics University of California, San Diego La Jolla, CA United States |
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| Fangyang Zheng | |
| School of Mathematical
Sciences Chongqing Normal University Chongqing China |
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