Scalar curvature, Kodaira dimension and A-genus

2017/06/04 by Yang, Xiaokui · 3 citations
#14F17 #32L25 #53A30 #53C55 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1706.01122

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 κ(X,J)=-∞. We also introduce the complex Yamabe number λ_c(X) for compact complex manifold X, and show that if λ_c(X)>0, then κ(X)=-∞; moreover, if X is also spin, then the Hirzebruch A-hat genus A(X)=0.

Cited by

• Chern number identities on compact complex surfaces and applications
• Comparison theorems in Hermitian geometry I
• Conformal extremal metrics and constant scalar curvature

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