Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Birationality of \'etale morphisms via surgery   We use a counting argument and surgery theory to show that if $D$ is a
sufficiently general algebraic hypersurface in $\Bbb C^n$, then any local
diffeomorphism $F:X \to \Bbb C^n$ of simply connected manifolds which is a
$d$-sheeted cover away from $D$ has degree $d=1$ or $d=\infty$ (however all
degrees $d > 1$ are possible if $F$ fails to be a local diffeomorphism at even
a single point). In particular, any \'etale morphism $F:X \to \Bbb C^n$ of
algebraic varieties which covers away from such a hypersurface $D$ must be
birational.

10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin