no. 4
Generic subgroups of Aut đ”č n
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 4, pp. 851-868.

We prove that for a parabolic subgroup Γ of Aut đ”č n the fixed points sets of all elements in Γ∖{ id đ”č n } are the same. This result, together with a deep study of the structure of subgroups of Aut đ”č n acting freely and properly discontinuously on đ”č n , entails a generalization of the so called weak Hurwitz’s theorem: namely that, given a complex manifold X covered by đ”č 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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de Fabritiis, Chiara. Generic subgroups of Aut $\mathbb {B}^n$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 4, pp. 851-868. http://archive.numdam.org/item/ASNSP_2002_5_1_4_851_0/

[1] M. Abate:, “Iteration theory of holomorphic maps on taut manifolds”, Mediterranean Press, Rende, Cosenza 1989. | MR | Zbl

[2] M. Abate - J.-P. Vigué, Common fixed points in hyperbolic Riemann surfaces and convex domains, Proc. Amer. Math. Soc. 112 (1991), 503-512. | MR | Zbl

[3] F. Bracci, Common fixed points of commuting holomorphic maps in the unit ball of ℂ n , Proc. Amer. Math. Soc. 127, 4, (1999), 1133-1141. | MR | Zbl

[4] C. De Fabritiis, Commuting holomorphic functions and hyperbolic automorphisms, Proc. Amer. Math. Soc. 124 (1996), 3027-3037. | MR | Zbl

[5] C. De Fabritiis - G. Gentili, On holomorphic maps which commute with hyperbolic automorphisms, Adv. Math. 144 (1999), 119-136. | MR | Zbl

[6] C. De Fabritiis - A. Iannuzzi, Quotients of the unit ball of ℂ n by a free action of â„€, Jour. d'Anal. Math. 85 (2001), 213-224. | MR | Zbl

[7] H. M. Farkas - I. Kra, “Riemann Surfaces”, Springer, Berlin, 1980. | MR | Zbl

[8] T. Franzoni - E. Vesentini, “Holomorphic maps and invariant distances”, North-Holland, Amsterdam, 1980. | MR | Zbl

[9] M. H. Heins, A generalization of the Aumann-Carathéodory Starrheitssatz, Duke Math. J. 8 (1941), 312-316. | JFM | MR

[10] A. Hurwitz, Über algebraische Gebilde mit eindeutingen Transformationen in sich, Math. Ann. 41 (1893), 403-442. | JFM | MR

[11] I. Kra, “Automorphic forms and Kleinian groups”, Beinjamin, New York, 1972. | MR | Zbl

[12] B. Maccluer, Iterates of holomorphic self-maps of the unit ball of ℂ n , Mich. Math. J. 30 (1983), 97-106. | MR | Zbl

[13] W. Rudin, “Function theory in the Unit Ball of ℂ n ”, Springer, Berlin 1980. | MR | Zbl