Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the characterization of abelian varieties for log pairs in zero and
  positive characteristic   Let $(X,\Delta)$ be a pair. We study how the condition $\kappa(K_X +
\Delta)=0$ causes surjectivity or birationality of the Albanese map and the
Albanese morphism of $X$ in both characteristic $0$ and characteristic $p > 0$.
In particular in characteristic $0$ we generalize Kawamata's result to the
cases of log canonial pairs, and in characteristic $p>0$ we generalize a result
of Hacon-Patakfalvi to the cases of log pairs. Moreover we show that if $X$ is
a normal projective threefold in characteristic $p>0$, the coefficients of the
components of $\Delta$ are $\le 1$ and $-(K_X+\Delta)$ is semiample, then the
Albanese morphism of $X$ is surjective under reasonable assumptions on $p$ and
the singularities of the general fibers of the Albanese morphism. This is a
positive characteristic analog in dimension 3 of a result of Zhang on a
conjecture of Demailly-Peternell-Schneider.

26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat