Generic subgroups of Aut \mathbb{B}^n

• Chiara de Fabritiis ^[1]
  1. [1] Università degli Studi de Ancona
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 1, Nº 4, 2002, págs. 851-868
• Idioma: inglés
• Enlaces
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• Resumen

  • 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 ${\rm Hol}(X,X)$.