Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Notes on automorphisms of surfaces of general type with $p_g=0$ and
  $K^2=7$   Let $S$ be a smooth minimal complex surface of general type with $p_g=0$ and
$K^2=7$. We prove that any involution on $S$ is in the center of the
automorphism group of $S$. As an application, we show that the automorphism
group of an Inoue surface with $K^2=7$ is isomorphic to $\mathbb{Z}_2^2$ or
$\mathbb{Z}_2 \times \mathbb{Z}_4$. We construct a $2$-dimensional family of
Inoue surfaces with automorphism groups isomorphic to $\mathbb{Z}_2 \times
\mathbb{Z}_4$.

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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: econ
13
The categories of this paper are: quant-ph
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The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an