Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Pluri-canonical Systems of Arithmetic Surfaces   Let $S$ be a Dedekind scheme with perfect residue fields at closed points,
let $f: X\rightarrow S$ be a minimal regular arithmetic surface of fibre genus
at least $2$ and let $f': X'\rightarrow S$ be the canonical model of $f$. It is
well known that $\omega_{X'/S}$ is relatively ample. In this paper we prove
that $\omega_{X'/S}^{\otimes n}$ is relative very ample for all $n\geq 3$.

15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg