Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Numerically Effective Log Canonical Divisors   Let $(X,\Delta)$ be a 4-dimensional log variety which is proper over the
field of complex numbers and with only divisorial log terminal singularities.
The log canonical divisor $K_X+\Delta$ is semi-ample, if it is nef (numerically
effective) and the Iitaka dimension $\kappa(X,K_X+\Delta)$ is strictly
positive. For the proof, we use Fujino's abundance theorem for semi log
canonical threefolds.

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The categories of this paper are: q-bio
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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: stat
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph