Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Existence of rational curves on algebraic varieties, minimal rational
  tangents, and applications
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci