On the automorphism groups of algebraic bounded domains
| dc.creator | Zaitsev, Dmitri | |
| dc.date | 1994-10-25 | |
| dc.date.accessioned | 2026-07-07T09:06:15Z | |
| dc.date.available | 2026-07-07T09:06:15Z | |
| dc.description | Let $D$ be a bounded domain in $C^n$. By the theorem of H.~Cartan, the group $Aut(D)$ of all biholomorphic automorphisms of $D$ has a unique structure of a real Lie group such that the action $Aut(D)\times D\to D$ is real analytic. This structure is defined by the embedding $C_v\colon Aut(D)\hookrightarrow D\times Gl_n(C)$, $f\mapsto (f(v), f_{*v})$, where $v\in D$ is arbitrary. Here we restrict our attention to the class of domains $D$ defined by finitely many polynomial inequalities. The appropriate category for studying automorphism of such domains is the Nash category. Therefore we consider the subgroup $Aut_a(D)\subset Aut(D)$ of all algebraic biholomorphic automorphisms which in many cases coincides with $Aut(D)$. Assume that $n>1$ and $D$ has a boundary point where the Levi form is non-degenerate. Our main result is theat the group $Aut_a(D)$ carries a unique structure of an affine Nash group such that the action $Aut_a(D)\times D\to D$ is Nash. This structure is defined by the embedding $C_v\colon Aut_a(D)\hookrightarrow D\times Gl_n(C)$ and is independent of the choice of $v\in D$. | |
| dc.description | 29 pages, LaTeX, Mathematischen Annalen, to appear | |
| dc.identifier | https://arxiv.org/abs/alg-geom/9410025 | |
| dc.identifier | http://arxiv.org/abs/alg-geom/9410025 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/149942 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Complex Variables | |
| dc.title | On the automorphism groups of algebraic bounded domains | |
| dc.type | text |