Quasi-negative holomorphic sectional curvature and positivity of the canonical bundle

By Simone Diverio, Stefano Trapani. Journal of differential geometry, 2016

71 citations recorded by the source corpus.

We show that if a compact complex manifold admits a K\"ahler metric whose holomorphic sectional curvature is everywhere non positive and strictly negative in at least one point, then its canonical bundle is positive.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7918c0e48ab51e59376a838e95bc82bc6b34a766

How researchers see this paper

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In Applied Mathematics

1. Fang Zheng
2. Xiaokui Yang
3. Quanting Zhao
4. Valentino Tosatti
5. Lei Ni

In Geometry and Topology

1. Fang Zheng
2. Xiaokui Yang
3. Quanting Zhao
4. Valentino Tosatti
5. Lei Ni

Citations in the corpus

• On real bisectional curvature for Hermitian manifolds (2016, background): “Ric(g) + √ −1∂∂uε satisfies ωn ε = euεωn, or equivalently, (33) Ric(ωε) = Ric(g) − √ −1∂∂uε = −ωε +εω, and uε ≤ Cfor such constant Cindependent of ε. The same proof of the inequality cn 1(KM) >0 in [7] will go through provided that, for each ε>0, there will be smooth function Sε >0 on Msuch ”