Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On general type surfaces with $q=1$ and $c_2 = 3 p_g$   Let $S$ be a minimal surface of general type with irregularity $q(S) = 1$.
Well-known inequalities between characteristic numbers imply that $3 p_g(S) \le
c_2(S) \le 10 p_g(S)$, where $p_g(S)$ is the geometric genus and $c_2(S)$ the
topological Euler characteristic. Surfaces achieving equality for the upper
bound are classified, starting with work of Debarre. We study equality in the
lower bound, showing that for each $n \ge 1$ there exists a surface with $q =
1$, $p_g = n$, and $c_2 = 3n$. The moduli space $\mathcal{M}_n$ of such
surfaces is a finite set of points, and we prove that $\#\mathcal{M}_n \to
\infty$ as $n \to \infty$. Equivalently, this paper studies the number of
closed complex hyperbolic $2$-manifolds of first betti number $2$ as a function
of volume; in particular, such a manifold exists for every possible volume.

3
The categories of this paper are: physics
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat