Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The geometry of some parameterizations and encodings   We explore parameterizations by radicals of low genera algebraic curves. We
prove that for $q$ a prime power that is large enough and prime to $6$, a fixed
positive proportion of all genus 2 curves over the field with $q$ elements can
be parameterized by $3$-radicals. This results in the existence of a
deterministic encoding into these curves when $q$ is congruent to $2$ modulo
$3$. We extend this construction to parameterizations by $\ell$-radicals for
small odd integers $\ell$, and make it explicit for $\ell=5$.

21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an