Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundedness of varieties of Fano type with alpha-invariants and volumes
  bounded below   We show that fixed dimensional klt weak Fano pairs with alpha-invariants and
volumes bounded away from $0$ and the coefficients of the boundaries belong to
the set of hyperstandard multiplicities $\Phi(\mathscr{R})$ associated to a
fixed finite set $\mathscr{R}$ form a bounded family. We also show
$\alpha(X,B)^{d-1}\mathrm{vol}(-(K_X+B))$ are bounded from above for all klt
weak Fano pairs $(X,B)$ of a fixed dimension $d$.

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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org