Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The decomposition groups of plane conics and plane rational cubics   The decomposition group of an irreducible plane curve $X\subset\mathbb P^2$
is the subgroup $\mathrm{Dec}(X)\subset\mathrm{Bir}(\mathbb P^2)$ of birational
maps which restrict to a birational map of $X$. We show that $\mathrm{Dec}(X)$
is generated by its elements of degree $\leq2$ when $X$ is either a conic or
rational cubic curve.

27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs