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manuscripta mathematica

, Volume 32, Issue 1–2, pp 59–80 | Cite as

Primitive holomorphic maps of curves

  • David Prill
Article
  • 28 Downloads

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.

Keywords

Number Theory Holomorphic Function Algebraic Geometry Topological Group Proper Morphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    ABHYANKAR, S. S., SINGH, B.: Embeddings of certain curves in the affine plane, Am. J. Math.100, 99–175 (1978)Google Scholar
  2. [2]
    AHLFORS, L.:Complex Analysis. 1st edn, New York: Mc-Graw Hill 1953Google Scholar
  3. [3]
    ALLING, N. L.: Extensions of meromorphic function rings over non-compact Riemann surfaces I, Math. Z.89, 273–299 (1965)Google Scholar
  4. [4]
    LANG, S.:Algebra. 1st edn, Reading, Mass.: Addison-Wesley 1965Google Scholar
  5. [5]
    LAX, R. F.: Weierstrass points of the universal curve, Math. Ann.216, 35–42 (1975)Google Scholar
  6. [6]
    MURTHY, P. and TOWBER, J.: Algebraic vector bundles over A3 are trivial, Invent. math.24, 173–189 (1974)Google Scholar
  7. [7]
    PATT, C.: Variations of Teichmüller and Torelli surfaces, J. Analyse Math.11, 221–247 (1963)Google Scholar
  8. [8]
    RINKHAM, H.: Deformations of algebraic varieties with Gm action, Asterisque20, 1–131 (1974)Google Scholar
  9. [9]
    RAUCH, H.: Weierstrass points, branch points and moduli of Riemann surfaces, Comm. Pure Appl. Math.12, 543–560 (1959)Google Scholar
  10. [10]
    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 1965Google Scholar
  11. [11]
    ROYDEN, H. L.: Rings of meromorphic functions, Proc. Amer. Math. Soc.9, 959–965 (1958)Google Scholar
  12. [12]
    SATHAYE, A.: On planar curves, Am. J. Math.99, 1105–1135 (1977)Google Scholar
  13. [13]
    SERRE, J-P.: Sur les modules projectifs, Séminaire Dubreil-Pisot: Algèbre et théorie des nombres (1960/61)Google Scholar
  14. [14]
    STOUT, E. L.: Extensions of rings of holomorphic functions, Math. Ann.196, 959–965 (1972)Google Scholar
  15. [15]
    STUTZ, J.: Primitive elements for modules over O (Y), Duke Math. J.41, 329–331 (1974)Google Scholar
  16. [16]
    TSANOV, V. V.: On hyperelliptic Riemann surfaces and doubly generated function algebras, C. R. Acad. Bulgare Sci.31, 1249–1252 (1978)Google Scholar
  17. [17]
    WEIL, A.: Über Matrizenringe auf Riemannschen Flächen und den Riemann-Rochschen Staz, Abh. math. Sem. Univ. Hamburg11, 110–115 (1936)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • David Prill
    • 1
  1. 1.Department of MathematicsUniversity of RochesterRochesterUSA

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