Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Noether-Lefschetz theorem for varieties of r-planes in complete
  intersections   Let X be a very general complete intersection in complex projective space and
we denote by $F_r(X)$ the variety of r-planes in X, for $r\geq 1$. We show that
the Picard number of $F_r(X)$ is 1, as soon as $\dim F_r(X)\geq 2$, except when
X is a quadric of dimension 2r or 2r+2, or X is a complete intersection of two
quadrics of dimension 2r+2. We also apply this result to determine the
cohomology class of the variety of planes of a cubic fivefold contained (by the
Abel-Jacobi map) in the intermediate Jacobian.

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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
1
The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat