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arXiv · 1706.01122

Scalar curvature, Kodaira dimension and $\hat A$-genus

Xiaokui Yang
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Abstract

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 canonical bundle $K_X$ is not pseudo-effective and the Kodaira dimension $\kappa(X,J)=-\infty$. We also introduce the complex Yamabe number $\lambda_c(X)$ for compact complex manifold $X$, and show that if $\lambda_c(X)>0$, then $\kappa(X)=-\infty$; moreover, if $X$ is also spin, then the Hirzebruch $A$-hat genus $\hat A(X)=0$.

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Xiaokui Yang. 2017-06-04. Scalar curvature, Kodaira dimension and $\hat A$-genus. https://arxiv.org/abs/1706.01122

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