Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effective bound of linear series on arithmetic surfaces   We prove an effective upper bound on the number of effective sections of a
hermitian line bundle over an arithmetic surface. It is an effective version of
the arithmetic Hilbert--Samuel formula in the nef case. As a consequence, we
obtain effective lower bounds on the Faltings height and on the
self-intersection of the canonical bundle in terms of the number of singular
points on fibers of the arithmetic surface.

16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex