Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: K-stability of birationally superrigid Fano 3-fold weighted
  hypersurfaces   We prove that the alpha invariant of a quasi-smooth Fano 3-fold weighted
hypersurface of index $1$ is greater than or equal to $1/2$. Combining this
with the result of Stibitz and Zhuang \cite{SZ19} on a relation between
birational superrigidity and K-stability, we prove the K-stability of a
birationally superrigid quasi-smooth Fano 3-fold weighted hypersurfaces of
index $1$.

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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: gr-qc