Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An integral version of Zariski decompositions on normal surfaces   We show that any pseudo-effective divisor on a normal surface decomposes
uniquely into its "integral positive" part and "integral negative" part, which
is an integral analog of Zariski decompositions. By using this decomposition,
we give three applications: a vanishing theorem of divisors on surfaces (a
generalization of Kawamata-Viehweg and Miyaoka vanishing theorems), Reider-type
theorems of adjoint linear systems on surfaces (including a log version and a
relative version of the original one) and extension theorems of morphisms
defined on curves on surfaces (generalizations of Serrano and Paoletti's
results).

37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol