Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A simple proof for the existence of Zariski decompositions on surfaces   In this note we give a quick and simple proof of the existence (and
uniqueness) of Zariski decompositions on surfaces. While Zariski's original
proof employs a rather sophisticated procedure to construct the negative part
of the decomposition, the present approach is based on the idea that the
positive part can be constructed from a maximality condition. It may also be
useful that this approach yields a practical algorithm for the computation of
the positive part.

17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con