Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Birational models of ${\mathcal M}_{2,2}$ arising as moduli of curves
  with nonspecial divisors   We study birational projective models of ${\mathcal M}_{2,2}$ obtained from
the moduli space of curves with nonspecial divisors. We describe geometrically
which singular curves appear in these models and show that one of them is
obtained by blowing down the Weierstrass divisor in the moduli stack of
${\mathcal Z}$-stable curves $\overline{\mathcal M}_{2,2}({\mathcal Z})$
defined by Smyth. As a corollary, we prove projectivity of the coarse moduli
space $\overline{M}_{2,2}({\mathcal Z})$.

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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph