We prove that constant scalar curvature Kähler (cscK) manifolds with transcendental cohomology class are K-semistable, naturally generalising the situation for polarised manifolds. Relying on a recent result by R. Berman, T. Darvas and C. Lu regarding properness of the K-energy, it moreover follows that cscK manifolds with discrete automorphism group are uniformly K-stable. As a main step of the proof we establish, in the general Kähler setting, a formula relating the (generalised) Donaldson–Futaki invariant to the asymptotic slope of the K-energy along weak geodesic rays.

中文翻译：

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具有先验同调类的cscK流形的K-Semistability。

我们证明具有先验同调性类的恒定标量曲率Kähler（cscK）流形是K半准的，自然地推广了极化流形的情况。依靠R. Berman，T。Darvas和C. Lu关于K能量的正确性的最新结果，得出的结论是具有离散自同构群的cscK流形一致地是K稳定的。作为证明的主要步骤，我们在一般的Kähler环境中建立一个公式，将（广义的）Donaldson–Futaki不变量与沿着弱测地线的K能量的渐近斜率相关。