Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An algebraic proof of Iitaka's Conjecture C_{2,1}   We give a proof of Iitaka's Conjecture C_{2,1} using only elementary methods
from algebraic geometry. The main point is that, given a non-isotrivial and
relatively minimal family f : X \to B, where X is a surface and B is a curve,
both smooth and projective, we show that the direct image of the relatively
canonical sheaf has strictly positive degree.

17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int