Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Unirationality of Hurwitz spaces of coverings of degree <= 5   Let $Y$ be a smooth, projective curve of genus $g\geq 1$ over the complex
numbers. Let $H^0_{d,A}(Y)$ be the Hurwitz space which parametrizes coverings
$p:X \to Y$ of degree $d$, simply branched in $n=2e$ points, with monodromy
group equal to $S_d$, and $det(p_{*}O_X/O_Y)$ isomorphic to a fixed line bundle
$A^{-1}$ of degree $-e$. We prove that, when $d=3, 4$ or $5$ and $n$ is
sufficiently large (precise bounds are given), these Hurwitz spaces are
unirational. If in addition $(e,2)=1$ (when $d=3$), $(e,6)=1$ (when $d=4$) and
$(e,10)=1$ (when $d=5$), then these Hurwitz spaces are rational.

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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: quant-ph
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The categories of this paper are: stat