# Stability of valuations and Kollár components

@article{Li2016StabilityOV, title={Stability of valuations and Koll{\'a}r components}, author={Chi Li and Xu Chen}, journal={arXiv: Algebraic Geometry}, year={2016} }

We prove that among all Kollar components obtained by plt blow ups of a klt singularity $o \in (X, D)$, there is at most one that is (log-)K-semistable. We achieve this by showing that if such a Kollar component exists, it uniquely minimizes the normalized volume function introduced in [Li15a] among all divisorial valuations. Conversely, we show any divisorial minimizer of the normalized volume function yields a K-semistable Kollar component. We also prove that for any klt singularity, the…

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