Generic subgroups of Aut 𝔹 n

Chiara de Fabritiis

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 4, page 851-868
  • ISSN: 0391-173X

Abstract

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We prove that for a parabolic subgroup Γ of Aut 𝔹 n the fixed points sets of all elements in Γ ∖ { id 𝔹 n } are the same. This result, together with a deep study of the structure of subgroups of Aut 𝔹 n acting freely and properly discontinuously on 𝔹 n , entails a generalization of the so called weak Hurwitz’s theorem: namely that, given a complex manifold X covered by 𝔹 n and such that the group of deck transformations of the covering is “sufficiently generic”, then id X is isolated in Hol ( X , X ) .

How to cite

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de Fabritiis, Chiara. "Generic subgroups of Aut $\mathbb {B}^n$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.4 (2002): 851-868. <http://eudml.org/doc/84489>.

@article{deFabritiis2002,
abstract = {We prove that for a parabolic subgroup $\Gamma $ of $\{\rm Aut\} \mathbb \{B\}^n $ the fixed points sets of all elements in $\Gamma \setminus \lbrace \{\rm id\}_\{\{\mathbb \{B\}\}^n\}\rbrace $ are the same. This result, together with a deep study of the structure of subgroups of $\{\rm Aut\} \mathbb \{B\}^n $ acting freely and properly discontinuously on $ \mathbb \{B\}^n $, entails a generalization of the so called weak Hurwitz’s theorem: namely that, given a complex manifold $X$ covered by $ \mathbb \{B\}^n $ and such that the group of deck transformations of the covering is “sufficiently generic”, then $\{\rm id\}_X$ is isolated in $\{\rm Hol\}(X,X)$.},
author = {de Fabritiis, Chiara},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
language = {eng},
number = {4},
pages = {851-868},
publisher = {Scuola normale superiore},
title = {Generic subgroups of Aut $\mathbb \{B\}^n$},
url = {http://eudml.org/doc/84489},
volume = {1},
year = {2002},
}

TY - JOUR
AU - de Fabritiis, Chiara
TI - Generic subgroups of Aut $\mathbb {B}^n$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 4
SP - 851
EP - 868
AB - We prove that for a parabolic subgroup $\Gamma $ of ${\rm Aut} \mathbb {B}^n $ the fixed points sets of all elements in $\Gamma \setminus \lbrace {\rm id}_{{\mathbb {B}}^n}\rbrace $ are the same. This result, together with a deep study of the structure of subgroups of ${\rm Aut} \mathbb {B}^n $ acting freely and properly discontinuously on $ \mathbb {B}^n $, entails a generalization of the so called weak Hurwitz’s theorem: namely that, given a complex manifold $X$ covered by $ \mathbb {B}^n $ and such that the group of deck transformations of the covering is “sufficiently generic”, then ${\rm id}_X$ is isolated in ${\rm Hol}(X,X)$.
LA - eng
UR - http://eudml.org/doc/84489
ER -

References

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