Automorphism Groups of Compact Complex Surfaces: T-Jordan Property, Tits Alternative and Solvability
نویسندگان
چکیده
Let $X$ be a (smooth) compact complex surface. We show that the torsion subgroup of biholomorphic automorphism group $\operatorname{Aut}(X)$ is virtually nilpotent. Moreover, we study Tits alternative and virtual derived length solvable subgroups $\operatorname{Aut}(X)$.
منابع مشابه
Domains in complex surfaces with non - compact automorphism groups ✩
Let X be an arbitrary complex surface and D a domain in X that has a non-compact group of holomorphic automorphisms. A characterization of those domains D that admit a smooth, weakly pseudoconvex, finite type boundary orbit accumulation point is obtained. © 2007 Elsevier Inc. All rights reserved.
متن کاملJordan Groups and Automorphism Groups of Algebraic Varieties
The first section of this paper is focused on Jordan groups in abstract setting, the second on that in the settings of automorphisms groups and groups of birational self-maps of algebraic varieties. The appendix contains formulations of some open problems and the relevant comments. MSC 2010: 20E07, 14E07
متن کاملCompact automorphism groups of vertex operator algebras
Let V be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group G of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for G and the irreducible modules for V G which are contained in V where V G is the space of G-invariants of V. We also prove a concomitant Galois correspondence between vertex operator s...
متن کاملTits alternative for 3-manifold groups
Let M be an irreducible, orientable, closed 3-manifold with fundamental group G. We show that if the pro-p completion Ĝp of G is infinite then G is either soluble-by-finite or contains a free subgroup of rank 2.
متن کاملThe Tits alternative for generalised tetrahedron groups
A generalised tetrahedron group is the colimit of a triangle of groups whose vertex groups are generalised triangle groups and whose edge groups are finite cyclic. We prove an improved Spelling Theorem for generalised triangle groups which enables us to compute the precise Gersten-Stallings angles of this triangle of groups, and hence obtain a classification of generalised tetrahedron groups ac...
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: Journal of Geometric Analysis
سال: 2023
ISSN: ['1559-002X', '1050-6926']
DOI: https://doi.org/10.1007/s12220-023-01268-z