Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Construction of noncommutative surfaces with exceptional collections of
  length 4   Recently de Thanhoffer de V\"olcsey and Van den Bergh classified the Euler
forms on a free abelian group of rank 4 having the properties of the Euler form
of a smooth projective surface. There are two types of solutions: one
corresponding to $\mathbb{P}^1\times\mathbb{P}^1$ (and noncommutative
quadrics), and an infinite family indexed by the natural numbers. For $m=0,1$
there are commutative and noncommutative surfaces having this Euler form,
whilst for $m\geq 2$ there are no commutative surfaces. In this paper we
construct sheaves of maximal orders on surfaces having these Euler forms,
giving a geometric construction for their numerical blowups.

1
The categories of this paper are: cs
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin