Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: k-nets embedded in a projective plane over a field   We investigate $k$-nets with $k\geq 4$ embedded in the projective plane
$PG(2,\mathbb{K})$ defined over a field $\mathbb{K}$; they are line
configurations in $PG(2,\mathbb{K})$ consisting of $k$ pairwise disjoint
line-sets, called components, such that any two lines from distinct families
are concurrent with exactly one line from each component. The size of each
component of a $k$-net is the same, the order of the $k$-net. If $\mathbb{K}$
has zero characteristic, no embedded $k$-net for $k\geq 5$ exists; see [1,2].
Here we prove that this holds true in positive characteristic $p$ as long as
$p$ is sufficiently large compared with the order of the $k$-net. Our approach,
different from that used in [1,2], also provides a new proof in characteristic
zero.
  [1] J. Stipins, Old and new examples of k-nets in P2, math.AG/0701046.
  [2] S. Yuzvinsky, A new bound on the number of special fibers in a pencil of
curves, Proc. Amer. Math. Soc. 137 (2009), 1641-1648.

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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat