Arc K-semistability is claimed to be a very general algebraic property in flat families via openness of Paul-stability of pairs, but the proof of the pair-stability lemma contains a false assertion about orbit-closure fibers.
Uniqueness of K -polystable degenerations of F ano varieties
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The constant scalar curvature K\"ahler condition is very general
Arc K-semistability is claimed to be a very general algebraic property in flat families via openness of Paul-stability of pairs, but the proof of the pair-stability lemma contains a false assertion about orbit-closure fibers.