Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform families of minimal rational curves on Fano manifolds   It is a well-known fact that families of minimal rational curves on rational
homogeneous manifolds of Picard number one are uniform, in the sense that the
tangent bundle to the manifold has the same splitting type on each curve of the
family. In this note we prove that certain --stronger-- uniformity conditions
on a family of minimal rational curves on a Fano manifold of Picard number one
allow to prove that the manifold is homogeneous.

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The categories of this paper are: atom-ph
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
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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: patt-sol
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th