Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Three-fold divisorial contractions to singularities of higher indices
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph