Any big line bundle admits a special Fujita approximation, which is used to solve the uniform Yau-Tian-Donaldson conjecture: a polarized smooth projective variety admits a cscK metric iff it is Aut°(X,L)-uniformly K-stable.
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A solution to the Yau-Tian-Donaldson Conjecture through Special Fujita Approximations
Any big line bundle admits a special Fujita approximation, which is used to solve the uniform Yau-Tian-Donaldson conjecture: a polarized smooth projective variety admits a cscK metric iff it is Aut°(X,L)-uniformly K-stable.