K-polystability and reduced uniform K-stability of log Fano cone singularities
Abstract
We prove that a log Fano cone (X,,0) satisfying δT(X,,0) 1 is K-polystable for normal test configurations if and only if it is K-polystable for special test configurations. We also establish the reduced uniform K-stability of (X,,0) and show that it is equivalent to K-polystability.
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