Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $\overline{\mathcal{R}}_{15}$ is of general type   We prove that the moduli space $\overline{\mathcal{R}}_{15}$ of Prym curves
of genus $15$ is of general type. To this end we exhibit a virtual divisor
$\overline{\mathcal{D}}_{15}$ on $\overline{\mathcal{R}}_{15}$ as the
degeneracy locus of a globalized multiplication map of sections of line
bundles. We then proceed to show that this locus is indeed of codimension one
and calculate its class. Using this class, we can conclude that
$K_{\overline{\mathcal{R}}_{15}}$ is big. This complements a 2010 result of
Farkas and Ludwig: now the spaces $\overline{\mathcal{R}}_g$ are known to be of
general type for $g \geq 14$.

18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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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: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex