Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Birational maps of 3-folds   We show that 3-fold terminal flips and divisorial contractions may be
factored into a sequence of flops, blow-downs to a smooth curve in a smooth
3-fold or divisorial contractions to points with minimal discrepancies.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess