Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Balanced line bundles on Fano varieties   A conjecture of Batyrev and Manin relates arithmetic properties of varieties
with ample anticanonical class to geometric invariants; in particular, counting
functions defined by metrized ample line bundles and the corresponding
asymptotics of rational points of bounded height are interpreted in terms of
cones of effective divisors and certain thresholds with respect to these cones.
This framework leads to the notion of balanced line bundles, whose counting
functions, conjecturally, capture generic distributions of rational points. We
investigate balanced line bundles in the context of the Minimal Model Program,
with special regard to the classification of Fano threefolds.

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The categories of this paper are: q-alg
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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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: q-fin