Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Symmetrization of Rational Maps: Arithmetic Properties and Families of
  Latt\`es Maps of $\mathbb P^k$   In this paper we study properties of endomorphisms of $\mathbb P^k$ using a
symmetric product construction $(\mathbb P^1)^k/\mathfrak{S}_k \cong \mathbb
P^k$. Symmetric products have been used to produce examples of endomorphisms of
$\mathbb P^k$ with certain characteristics, $k\geq2$. In the present note, we
discuss the use of these maps to enlighten arithmetic phenomena and stability
phenomena in parameter spaces. In particular, we study notions of uniform
boundedness of rational preperiodic points via good reduction information,
$k$-deep postcritically finite maps, and characterize families of Latt\`es
maps.

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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc