Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability of Valuations and Koll\'ar Components   We prove that among all Koll\'ar 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 Koll\'ar 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 Koll\'ar component. We also
prove that for any klt singularity, the infimum of the normalized function is
always approximated by the normalized volumes of Koll\'ar components.

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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga