Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational Fibrations of $\bar{M}_{5,1}$ and $\bar{M}_{6,1}$   This is the second of two papers on the birational geometry of
$\bar{M}_{g,1}$. We construct rational maps from $\bar{M}_{5,1}$ and
$\bar{M}_{6,1}$ to lower-dimensional moduli spaces. As a consequence, we
identify geometric divisors that generate extremal rays of the effective cones
for these spaces.

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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph