Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On rigid germs of finite morphisms of smooth surfaces   We prove that a germ of a finite morphism of smooth surfaces is rigid if the
germ of its branch curve has one of $ADE$-singularity types and establish a
correspondence between the set of rigid germs and the set of Belyi rational
functions $f\in \bar{\mathbb Q}(z)$.

3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat