Algebraically hyperbolic manifolds have finite automorphism groups
نویسندگان
چکیده
منابع مشابه
On the Automorphism Groups of Hyperbolic Manifolds
We show that there does not exist a Kobayashi hyperbolic complex manifold of dimension n 6= 3, whose group of holomorphic automorphisms has dimension n2 + 1 and that, if a 3-dimensional connected hyperbolic complex manifold has automorphism group of dimension 10, then it is holomorphically equivalent to the Siegel space. These results complement earlier theorems of the authors on the possible d...
متن کاملFinite Groups and Hyperbolic Manifolds
The isometry group of a compact n-dimensional hyperbolic man-ifold is known to be finite. We show that for every n ≥ 2, every finite group is realized as the full isometry group of some compact hyperbolic n-manifold. The cases n = 2 and n = 3 have been proven by Greenberg [G] and Ko-jima [K], respectively. Our proof is non constructive: it uses counting results from subgroup growth theory to sh...
متن کاملHyperbolic 2-Dimensional Manifolds with 3-Dimensional Automorphism Groups I
Let M be a Kobayashi-hyperbolic 2-dimensional complex manifold and Aut(M) the group of holomorphic automorphisms of M . We showed earlier that if dimAut(M) = 3, then Aut(M)-orbits are closed submanifolds in M of (real) codimension 1 or 2. In this paper we classify all connected Kobayashi-hyperbolic 2-dimensional manifolds with 3-dimensional automorphism groups in the case when every orbit has c...
متن کاملHyperbolic 2-Dimensional Manifolds with 3-Dimensional Automorphism Groups II
Let M be a Kobayashi-hyperbolic 2-dimensional complex manifold and Aut(M) the group of holomorphic automorphisms of M . We showed earlier that if dimAut(M) = 3, then Aut(M)-orbits are closed submanifolds in M of (real) codimension 1 or 2. In a preceding article we classified all such manifolds in the case when every orbit has codimension 1. In the present paper we complete the classification by...
متن کاملComplete hyperbolic Stein manifolds with prescribed automorphism groups
It is well known that the automorphism group of a hyperbolic manifold is a Lie group. Conversely, it is interesting to see whether or not any Lie group can be prescribed as the automorphism group of a certain complex manifold. When the Lie group G is compact and connected, this problem has been completely solved by Bedford–Dadok and independently by Saerens–Zame in 1987. They have constructed s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Contemporary Mathematics
سال: 2019
ISSN: 0219-1997,1793-6683
DOI: 10.1142/s0219199719500032