Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mixed quasi-\'etale surfaces, new surfaces of general type with $p_g=0$
  and their fundamental group   We call a projective surface $X$ mixed quasi-\'etale quotient if there exists
a curve $C$ of genus $g(C)\geq 2$ and a finite group $G$ that acts on $C\times
C$ exchanging the factors such that $X=(C\times C)/G$ and the map $C\times C
\rightarrow X$ has finite branch locus. The minimal resolution of its
singularities is called mixed quasi-\'etale surface. We study the mixed
quasi-\'etale surfaces under the assumption that $(C\times C)/G^0$ has only
nodes as singularities, where $G^0\triangleleft G$ is the index two subgroup of
the elements that do not exchange the factors. We classify the minimal regular
surfaces with $p_g=0$ whose canonical model is a mixed quasi-\'etale quotient
as above. All these surfaces are of general type and as an important byproduct,
we provide an example of a numerical Campedelli surface with topological
fundamental group $\bbZ_4$, and we realize 2 new topological types of surfaces
of general type. Three of the families we construct are $\bbQ$-homology
projective planes.

29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
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The categories of this paper are: adap-org
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
18
The categories of this paper are: econ