Abstract
Let t: X→Y be a proper morphism of non-singular irreducible affine curves over ℌ. This paper shows that there is seldom a holomorphic function f such that (t,f): X → Y × ℌ is a holomorphic embedding.
Similar content being viewed by others
References
ABHYANKAR, S. S., SINGH, B.: Embeddings of certain curves in the affine plane, Am. J. Math.100, 99–175 (1978)
AHLFORS, L.:Complex Analysis. 1st edn, New York: Mc-Graw Hill 1953
ALLING, N. L.: Extensions of meromorphic function rings over non-compact Riemann surfaces I, Math. Z.89, 273–299 (1965)
LANG, S.:Algebra. 1st edn, Reading, Mass.: Addison-Wesley 1965
LAX, R. F.: Weierstrass points of the universal curve, Math. Ann.216, 35–42 (1975)
MURTHY, P. and TOWBER, J.: Algebraic vector bundles over A3 are trivial, Invent. math.24, 173–189 (1974)
PATT, C.: Variations of Teichmüller and Torelli surfaces, J. Analyse Math.11, 221–247 (1963)
RINKHAM, H.: Deformations of algebraic varieties with Gm action, Asterisque20, 1–131 (1974)
RAUCH, H.: Weierstrass points, branch points and moduli of Riemann surfaces, Comm. Pure Appl. Math.12, 543–560 (1959)
RÖHRL, H.: Question 13 in appendix,Proceedings of the Conference on Complex Analysis, ed. A. Aeppli, E. Calabi, H. Röhrl. Berlin-Heidelberg-New York: Springer 1965
ROYDEN, H. L.: Rings of meromorphic functions, Proc. Amer. Math. Soc.9, 959–965 (1958)
SATHAYE, A.: On planar curves, Am. J. Math.99, 1105–1135 (1977)
SERRE, J-P.: Sur les modules projectifs, Séminaire Dubreil-Pisot: Algèbre et théorie des nombres (1960/61)
STOUT, E. L.: Extensions of rings of holomorphic functions, Math. Ann.196, 959–965 (1972)
STUTZ, J.: Primitive elements for modules over O (Y), Duke Math. J.41, 329–331 (1974)
TSANOV, V. V.: On hyperelliptic Riemann surfaces and doubly generated function algebras, C. R. Acad. Bulgare Sci.31, 1249–1252 (1978)
WEIL, A.: Über Matrizenringe auf Riemannschen Flächen und den Riemann-Rochschen Staz, Abh. math. Sem. Univ. Hamburg11, 110–115 (1936)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Prill, D. Primitive holomorphic maps of curves. Manuscripta Math 32, 59–80 (1980). https://doi.org/10.1007/BF01298182
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01298182