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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Scalar curvature on compact complex manifolds


Author: Xiaokui Yang
Journal: Trans. Amer. Math. Soc. 371 (2019), 2073-2087
MSC (2010): Primary 53C55, 32Q25, 32Q20
DOI: https://doi.org/10.1090/tran/7409
Published electronically: October 11, 2018
MathSciNet review: 3894045
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Abstract: In this paper, we prove that, a compact complex manifold $ X$ admits a smooth Hermitian metric with positive (resp., negative) scalar curvature if and only if $ K_X$ (resp., $ K_X^{-1}$) is not pseudo-effective. On the contrary, we also show that on an arbitrary compact complex manifold $ X$ with complex dimension $ \geq 2$, there exist smooth Hermitian metrics with positive total scalar curvature, and one of the key ingredients in the proof relies on a recent solution to the Gauduchon conjecture by G. Székelyhidi, V. Tosatti, and B. Weinkove.


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Additional Information

Xiaokui Yang
Affiliation: Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China — and — HCMS, CEMS, NCNIS, HLM, UCAS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
Email: xkyang@amss.ac.cn

DOI: https://doi.org/10.1090/tran/7409
Received by editor(s): July 1, 2017
Received by editor(s) in revised form: September 16, 2017
Published electronically: October 11, 2018
Additional Notes: This work was supported in part by China’s Recruitment Program of Global Experts and by Hua Loo-Keng Center for Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences.
Article copyright: © Copyright 2018 American Mathematical Society