Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toward the second main theorem on complements: from local to global   We prove the boundedness of complements modulo two conjectures:
Borisov-Alexeev conjecture and effective adjunction for fibre spaces. We
discuss the last conjecture and prove it in two particular cases.

8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg