Conjecture 1.2 (Yau-Tian-Donaldson) . [020C]

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Conjecture 1.2 (Yau-Tian-Donaldson).

Let $[\omega]=C_{1}({L})$ for some holomorphic line bundle $L$ on a Kähler manifold $M$ , then the underlying $(M,L)$ is K-stable if and only if there exists a constant scalar curvature Kähler metric in $[\omega]$ .