Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the geometry of anticanonical pairs   The systematic study of rational surfaces $Y$ with an anticanonical cycle $D$
dates back to a fundamental paper of Looijenga in 1981. Recently, Gross,
Hacking and Keel have introduced new ideas into the subject. The goal of this
mainly expository paper is to survey some results about such surfaces, old and
new. We discuss the birational geometry and deformation theory of such pairs as
well as the behavior of nef and big linear systems. We prove a theorem of
Torelli type due to Gross-Hacking-Keel and describe some consequences. Among
the new results in this paper are (1) a proof that the diffeomorphism type of a
pair $(Y,D)$ is the same as its deformation type, and (2) a new
characterization of the roots of the pair, i.e. the integral classes of square
$-2$ in $H^2(Y)$ orthogonal to the components of $D$ which become the class of
a smooth rational curve in some deformation.

36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int