Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Varieties of general type with the same Betti numbers as $\mathbb
  P^1\times \mathbb P^1\times\ldots\times \mathbb P^1$   We study quotients $\Gamma\backslash \mathbb H^n$ of the $n$-fold product of
the upper half plane $\mathbb H$ by irreducible and torsion-free lattices
$\Gamma < PSL_2(\mathbb R)^n$ with the same Betti numbers as the $n$-fold
product $(\mathbb P^1)^n$ of projective lines. Such varieties are called fake
products of projective lines or fake $(\mathbb P^1)^n$. These are higher
dimensional analogs of fake quadrics. In this paper we show that the number of
fake $(\mathbb P^1)^n$ is finite (independently of $n$), we give examples of
fake $(\mathbb P^1)^4$ and show that for $n>4$ there are no fake $(\mathbb
P^1)^n$ of the form $\Gamma\backslash \mathbb H^n$ with $\Gamma$ contained in
the norm-1 group of a maximal order of a quaternion algebra over a real number
field.

16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph