Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of Fundamental Groups of Galois Covers of Surfaces of
  Small Degree Degenerating to Nice Plane Arrangements   Let $X$ be a surface of degree $n$, projected onto $\mathbb{CP}^2$. The
surface has a natural Galois cover with Galois group $S_n.$ It is possible to
determine the fundamental group of a Galois cover from that of the complement
of the branch curve of $X.$ In this paper we survey the fundamental groups of
Galois covers of all surfaces of small degree $n \leq 4$, that degenerate to a
nice plane arrangement, namely a union of $n$ planes such that no three planes
meet in a line. We include the already classical examples of the quadric, the
Hirzebruch and the Veronese surfaces and the degree $4$ embedding of
$\mathbb{CP}^1 \times \mathbb{CP}^1,$ and also add new computations for the
remaining cases: the cubic embedding of the Hirzebruch surface $F_1$, the
Cayley cubic (or a smooth surface in the same family), for a quartic surface
that degenerates to the union of a triple point and a plane not through the
triple point, and for a quartic $4$-point. In an appendix, we also include the
degree $8$ surface $\mathbb{CP}^1\times \mathbb{CP}^1$ embedded by the $(2,2)$
embedding, and the degree $2n$ surface embedded by the $(1,n)$ embedding, in
order to complete the classification of all embeddings of $\mathbb{CP}^1 \times
\mathbb{CP}^1,$ which was begun in \cite{15}.

16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
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The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: hep-lat