Topic
Holomorphically separable
About: Holomorphically separable is a research topic. Over the lifetime, 20 publications have been published within this topic receiving 206 citations.
Papers
TL;DR: For example, Fornaess and Sibony as mentioned in this paper showed that f is not constant on any component fl(,~v), l> 0.2 on the Riemann surface.
Abstract: Riemann surface. As in Theorem 1.2 we show first that f is not constant on any component fl(,~v), l> 0. Hence we can assume using a diagonal process that for a subsequence (fm,),fm,~ h and h = ld on Ut~_of'(~_,p) c {q ~ g2; h(q) = q). Consequently U,~of'(~n) is closed in t2. Since fro, ~ ld on Zn and since f is not of finite order, see [FM], then f is conjugate to an irrational rotation on the Riemann surface E. We then show as in Theorem 2.3 of [FS3] that Z is contained in f2, so E is closed in I2. The rest of the argument is as in Theorem 1.2 or as in [FS3] Theorem 2.3. References [B] [BBD] [BS] [CG] [FM] [FS1] [FS2] [FS3] [FS4] [G] [HI [Ko] [Kr] [M] IN] [RR] [U] Beardon, A.: Iteration of rational functions. Springer Verlag (1991) Barrett, D., Bedford, E., Dadok, J.: T~-actions on holomorphically separable complex manifolds. Math. Z. 202 (1989), 65-82 Bedford, E., Smillie, J.: Polynomial diffeomorphisms of •2. II. Amer. J. Math. 4 (1991), 657-679 Carleson, L., Gamelin, T.: Complex dynamics. Springer Verlag (1993) Friedland, S., Milnor, J.: Dynamical properties of plane automorphisms. Ergodic theory and dynamical systems 9 (1989), 67-99 Fornaess, J.E., Sibony, N.: Complex dynamics in higher dimension. I. Asterisque 222 (1994), 201-231 Fornaess, J.E., Sibony, N.: Complex dynamics in higher dimension. II. To appear in Ann. Math. Studies Fornaess, J.E., Sibony, N.: Complex Henon mappings in 2 and Fatou-Bieberbach domains. Duke Math. J. 65 (1992), 345-380 Fornaess, J.E., Sibony, N.: Holomorphic dynamical systems. (To appear) Gavosto, E.: To appear Herman, M.: Recent results on some open questions on Siegel's linearization Kobayashi, S.: Hyperbolic manifolds and holomorphic mappings. New York, Marcel Dekker, 1970 Kruzhilin, N.G.: Holomorphic automorphisms of hyperbolic Reinhardt do- mains. Math. USSR Izvestya 32 (1989), 15-38 Milnor, J.: Dynamics in one complex variable: Introductory Lectures. SUNY Stony Brook. Institute for Mathematical Sciences. Preprint # 1990/5 Narashiman, R.: Several complex variables. Univ. Chicago Press, 1971 Rosay, J.-P., Rudin, W.: Holomorphic maps from IE n to C n. TAMS 310 (1988), 47-86 UEDA, T.: Fatou set in complex dynamics in projective spaces. Preprint
50 citations
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.org/legal.php) of a fichier do not necessarily imply a mention of copyright.
Abstract: © Annales de l’institut Fourier, 1986, tous droits réservés. L’accès aux archives de la revue « Annales de l’institut Fourier » (http://annalif.ujf-grenoble.fr/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
32 citations
1 May 1960
TL;DR: In this article, the authors considered the existence of holomorphic maps with a given rank on complex spaces countable at infinity and showed that the space of holomorphically separable spaces is K-complete.
Abstract: In ?3, we consider the existence of holomorphic maps with a given rank on complex spaces countable at infinity. We use the method given here to make a remark on an imbedding theorem for holomorphically complete spaces due to R. Remmert [4]. The author is indebted to Professor H. Cartan for his suggestions and for pointing out that the space of holomorphic functions is complete even for non-normal spaces. The author's thanks are due also to Professor K. Chandrasekharan for his encouragement prior to and during the preparation of this note. 2. We shall denote, throughout this note, the space of holomorphic functions on a complex space X, with the compact convergence topology, by R(X) =R. If X is holomorphically separable, it can be shown that X is Kcomplete (in the sense of [1 ]; we note that it is enough to have, for any xoCX, a holomorphic map f: X-->Ck such that xo is an isolated point of f'f(xo)), so that, by [1, Satz 8], X is countable at infinity. Hence R(X) is metrisable, and by [2, Satz 28], it is complete. We prove first
15 citations
TL;DR: In this paper, the authors define the codimension of the top non vanishing homology group of a manifold X with coefficients in Z2 to be the codemension of a homogeneous space X := G/H, where G is a connected complex Lie group and H is a closed complex subgroup.
Abstract: Define dx to be the codimension of the top non vanishing homology group of the manifold X with coefficients in Z2. We investigate homogeneous spaces X := G/H, where G is a connected complex Lie group and H is a closed complex subgroup for which dx = 1,2 and 0{X) / C. There exists a fibration 7r: G/H —> G/U such that G/U is holomorphically separable and n*(0(G/U)) = 0(G/H), see (11). We prove the following. If dx = 1, then F := U/H is compact and connected and Y :=G/U is an affine cone with its vertex removed. If dx = 2, then either F is connected with dp = 1 and Y is an affine cone with its vertex removed, or F is compact and connected and dy = 2, where Y is C, the affine quadric Q2, P2 — Q (with Q a quadric curve) or a homogeneous holomorphic C -bundle over an affine cone minus its vertex which is itself an algebraic principal bundle or which admits a two-to-one covering that is.
13 citations
TL;DR: In this paper, it was shown that the holomorphic automorphism groups of the spaces C k × (C * ) n - k and (C k - { 0 } ) × ( C * )n - k are not isomorphic as topological groups.
Abstract: In this paper, we prove that the holomorphic automorphism groups of the spaces C k × ( C * ) n - k and ( C k - { 0 } ) × ( C * ) n - k are not isomorphic as topological groups. By making use of this fact, we establish the following characterization of the space C k × ( C * ) n - k : Let M be a connected complex manifold of dimension n that is holomorphically separable and admits a smooth envelope of holomorphy. Assume that the holomorphic automorphism group of M is isomorphic to the holomorphic automorphism group of C k × ( C * ) n - k as topological groups. Then M itself is biholomorphically equivalent to C k × ( C * ) n - k . This was first proved by us in [5] under the stronger assumption that M is a Stein manifold.
10 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2017 | 2 |
| 2016 | 1 |
| 2015 | 1 |
| 2008 | 2 |
| 2006 | 3 |
| 2003 | 2 |