Abstract
We show that the family of the universal coverings of the fibers of a real analytic family \(\pi :X \to B \subset C^A \) of punctured compact Riemann surfaces is, locally w.r.t. B, bianalytically and on the fibers holomorphically a cartesian product.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abikoff, W.: The Real Analytic Theory of Teichmüller Spaces. Berlin, Heidelberg, New York. Springer 1980.
Grauert, H., Dethloff, G.: Deformation of Compact Riemann Surfaces Y of Genus p with Distinguished Points P 1,@@@, P m ∈ Y. In: Complex Geometry and Analysis; Proceedings of the International Symposium in Honour of E. Vesentini, Pisa 1988.
Kobayashi, S.: Intrinsic Distances, Measures and Geometric Function Theory. Bull. Am. Math. Soc. 82, 357–416 (1976)
Kodaira, K., Nierenberg, L., Spencer, D.C.: On the Existence of Deformations of Complex Analytic Structures. Ann. of Math. 68, 450–459 (1958)
Kodaira, K., Spencer, D.C.: On Deformation of Complex Analytic Structure I, II. Ann. of Math 67, 328–468 (1958)
Kodaira, K., Spencer, D.C.: A Theorem of Completeness for Complex Analytic Fiber Spaces. Acta Math. 100, 281–294 (1958)
Zaidenberg, M.G.: Stability of Hyperbolic Imbeddedness and Construction of Examples. Math. USSR Sbornik 63 No.2 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
About this paper
Cite this paper
Dethloff, G. (1991). Deformation of Compact Riemann Surfaces with Distinguished Points. In: Diederich, K. (eds) Complex Analysis. Aspects of Mathematics, vol 1. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-86856-5_17
Download citation
DOI: https://doi.org/10.1007/978-3-322-86856-5_17
Publisher Name: Vieweg+Teubner Verlag
Print ISBN: 978-3-322-86858-9
Online ISBN: 978-3-322-86856-5
eBook Packages: Springer Book Archive