Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: A sufficient condition for a toric weak Fano 4-fold to be deformed to a
  Fano manifold
30
The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin