Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Del Pezzo surfaces over finite fields   Let $X$ be a del Pezzo surface of degree $2$ or greater over a finite field
$\mathbb{F}_q$. The image $\Gamma$ of the Galois group
$\operatorname{Gal}(\overline{\mathbb{F}}_q / \mathbb{F}_q)$ in the group
$\operatorname{Aut}(\mathrm{Pic}(\overline{X}))$ is a cyclic subgroup
preserving the anticanonical class and the intersection form. The conjugacy
class of $\Gamma$ in the subgroup of
$\operatorname{Aut}(\mathrm{Pic}(\overline{X}))$ preserving the anticanonical
class and the intersection form is a natural invariant of $X$. We say that the
conjugacy class of $\Gamma$ in $\operatorname{Aut}(\mathrm{Pic}(\overline{X}))$
is the \textit{type} of a del Pezzo surface. In this paper we study which types
of del Pezzo surfaces of degree $2$ or greater can be realized for given $q$.
We collect known results about this problem and fill the gaps.

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The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat