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A characterization of the complex affine line. (English) Zbl 0864.14019
Summary: A characterization of affine nonsingular complex algebraic curves that are biregularly isomorphic to $$\mathbb{C}$$ is given; it is stated in terms of approximation of holomorphic maps by regular maps.
##### MSC:
 14H99 Curves in algebraic geometry 32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables 30E05 Moment problems and interpolation problems in the complex plane
##### Keywords:
curve biregularly isomorphic to $$\mathbb{C}$$
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##### References:
 [1] Bochnak, J., Coste, M., Roy, M-F.: Géometrie algébrique réelle. Ergebnisse der Math., vol.12, Berlin Heidelberg New York: Springer 1987. [2] Dold, A.: Lectures on Algebraic Topology. New York Heidelberg Berlin: Springer 1972. · Zbl 0234.55001 [3] Fosster, O.: Topologische Methoden in der Theorie Steinischer Räume. Actes, Congrès Intern. Math., 1970. Tome2, pp. 613–618, Gauthier-Villars, Paris 1971. [4] Grauert, H.: Holomorphe Funktionen mit Werten in komplexen Lieschen Gruppen. Math. Ann.133, 450–472 (1957). · Zbl 0080.29202 [5] Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero. Ann. of Math. (2)79, 109–326 (1964). · Zbl 0122.38603 [6] Kucharz, W.: The Runge approximation problem for holomorphic maps into Grassmannians. Math. Z.218, 343–348 (1995). · Zbl 0827.32015
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