Generic subgroups of Aut $\mathbb {B}^n$

de Fabritiis, Chiara

Generic subgroups of Aut

𝔹^{n}

de Fabritiis, Chiara

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 4, pp. 851-868.

Résumé

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 $Hol (X, X)$ .

Classification : 32A10, 32A40, 32H15, 32A30

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     author = {de Fabritiis, Chiara},
     title = {Generic subgroups of {Aut} $\mathbb {B}^n$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {851--868},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {4},
     year = {2002},
     mrnumber = {1991005},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2002_5_1_4_851_0/}
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de Fabritiis, Chiara. Generic subgroups of Aut $\mathbb {B}^n$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 4, pp. 851-868. http://www.numdam.org/item/ASNSP_2002_5_1_4_851_0/

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