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Scalar curvature, Kodaira dimension and \hat{A}-genus

Xiaokui Yang Department of Mathematics and Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China

Differential Geometry Algebraic Geometry mathscidoc:2206.10007

Mathematische Zeitschrift, 295, 365-380, 2019.6
Let (X, g) be a compact Riemannian manifold with quasi-positive Riemannian scalar curvature. If there exists a complex structure J compatible with g, then the Kodaira dimension of (X, J) is equal to −∞ and the canonical bundle KX is not pseudo-effective. We also introduce the complex Yamabe number λc(X) for compact complex manifold X, and show that if λ_c(X) is greater than 0, then κ(X) is equal to −∞; moreover, if X is also spin, then the Hirzebruch A-hat genus \hat{A}(X) is zero.
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@inproceedings{xiaokui2019scalar,
  title={Scalar curvature, Kodaira dimension and \hat{A}-genus},
  author={Xiaokui Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622155451749860452},
  booktitle={Mathematische Zeitschrift},
  volume={295},
  pages={365-380},
  year={2019},
}
Xiaokui Yang. Scalar curvature, Kodaira dimension and \hat{A}-genus. 2019. Vol. 295. In Mathematische Zeitschrift. pp.365-380. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220622155451749860452.
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