Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Virtual Cartier divisors and blow-ups
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci