# 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}
}
• Published 19 April 2016
• Mathematics
• arXiv: Algebraic Geometry
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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