Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random hypersurfaces and embedding curves in surfaces over finite fields   We use Poonen's closed point sieve to prove two independent results. First,
we show that the obvious obstruction to embedding a curve in a smooth surface
is the only obstruction over a perfect field, by proving the finite field
analogue of a Bertini-type result of Altman and Kleiman. Second, we prove a
conjecture of Vakil and Wood on the asymptotic probability of hypersurface
sections having a prescribed number of singularities.

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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: physics
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: nucl-ex