论文标题
$ \ textbf {aut} _ {\ textbf {hol}}（{\ bf \ mathbb c^n}）$
A canonical embedding of $\textbf{Aut}_{\textbf{hol}}({\bf \mathbb C^n})$
论文作者
论文摘要
组$ \ text {aut} _ {\ text {hol}}（\ mathbb c^n）$ by-biholomormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormormorphisms如果$ n = 1 $，则在较高的尺寸中，但在较高的大小对象中，它不是一个大的对象，它没有被明确描述。尽管当$ n> 1 $时涉及的复杂性，但令人惊讶的是，每个$ f \ in \ text {aut} _ {\ text {hol}}}（\ mathbb c^n）$在组内仅由两个数据，无限性和全球性质的数据唯一地确定。如果$ n = 1 $对于所有$ f $，此全局数据为零，然后仅由$ 1 $ -JET在$ 0 $确定，并且一个人恢复了$ \ text {aut} _ {\ text {hol text {hol}}}（\ mathbb c）= \ text = \ text {aff}（aff}（aff}（aff}（aftbb c））我们的主要结果被表述为$ \ text {aut} _ {\ text {hol}}}（\ Mathbb c^n）$的规范嵌入的存在，也从$ \ text {aut} _ {aut} _ {al text {hol}} {$ n）的$ \ text {aut} _ $ n）的自然候选人中挑选了自然候选。
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 $n>1$.
