Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Residual intersection theory with reducible schemes
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex