Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniruledness of some moduli spaces of stable pointed curves   We prove uniruledness of some moduli spaces $\bar{M}_{g,n}$ of stable curves
of genus $g$ with $n$ marked points using linear systems on nonsingular
projective surfaces containing the general curve of genus $g$. Precisely we
show that $\bar{M}_{g,n}$ is uniruled for $g=12$ and $n \leq 5$, $g=13$ and $n
\leq 3$, $g=15$ and $n \leq 2$. We then prove that the pointed hyperelliptic
locus $H_{g,n}$ is uniruled for $g \geq 2$ and $n \leq 4g+4$. In the last part
we show that a nonsingular complete intersection surface does not carry a
linear system containing the general curve of genus $g \geq 16$ and if it
carries a linear system containing the general curve of genus $12 \leq g \leq
15$ then it is canonical.

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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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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: ao-sci
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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: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph