Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lines on algebraic varieties   A variety $X$ is covered by lines if there exist a finite number of lines
contained in $X$ passing through each general point. I prove two theorems.
  Theorem 1:Let $X^n\subset P^M$ be a variety covered by lines. Then there are
at most $n!$ lines passing through a general point of $X$.
  Theorem 2:Let $X^n\subsetP^{n+1}$ be a hypersurface and let $x\in X$ be a
general point. If the set of lines having contact to order $k$ with $X$ at $x$
is of dimension greater than expected, then the lines having contact to order
$k$ are actually contained in $X$.

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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph