Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A canonical embedding of $\textbf{Aut}_{\textbf{hol}}({\bf \mathbb
  C^n})$   The group $\text{Aut}_{\text{hol}}(\mathbb C^n)$ of self-biholomorphisms of
$\mathbb C^n$ consists of affine maps if $n=1$, but in higher dimensions it is
a large object that has not been described explicitly. Despite the intricacies
involved when $n>1$, surprisingly every $F\in \text{Aut}_{\text{hol}}(\mathbb
C^n)$ is uniquely determined inside the group by only two data, of
infinitesimal and global nature: the $1$-jet of $F$ at $0$, and the complex
Hessian of a certain plurisubharmonic function associated to $F$. If $n=1$ this
global datum is zero for all $F$, which is then determined solely by its
$1$-jet at $0$, and one recovers $\text{Aut}_{\text{hol}}(\mathbb C)=
\text{Aff}(\mathbb C)\cong \mathbb C \times \mathbb C^{*}$. Our main result,
formulated as the existence of a canonical embedding of $
\text{Aut}_{\text{hol}} ( \mathbb C^n)$, also singles out a natural candidate
for moduli space of $ \text{Aut}_{\text{hol}} ( \mathbb C^n)$, for all $n>1$.

19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
12
The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat