Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds on the Picard rank of toric Fano varieties with minimal curve
  constraints   We study the Picard rank of smooth toric Fano varieties possessing families
of minimal rational curves of given degree. We discuss variants of a conjecture
of Chen-Fu-Hwang and prove a version of their statement that recovers the
original conjecture in sufficiently high dimension. We also prove new cases of
the original conjecture for high degrees in all dimensions. Our main tools come
from toric Mori theory and the combinatorics of Fano polytopes.

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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: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org