Skip to main content
Log in

Defining equations for cyclic prime covers of the Riemann sphere

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We determine a method to find explicit defining equations for each compact Riemann surface which admits a cyclic group of automorphisms C p of prime order p such that the quotient space has genus 0.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R. Brandt and H. Stichtenoth, Die Automorphismengruppen Hyperelliptischer Kurven, Manuscripta Mathematica 55 (1986), 83–92.

    Article  MATH  MathSciNet  Google Scholar 

  2. T. Breuer, Characters and Automorphism Groups of Compact Riemann Surfaces, Cambridge University Press, 2001.

  3. E. Bujalance, F. J. Cirre and M. D. E. Conder, On extendability of group actions on compact Riemann surfaces, Transactions of the American Mathematical Society 355 (2003), 1537–1557.

    Article  MATH  MathSciNet  Google Scholar 

  4. G. González-Díez, Loci of curves which are prime Galois coverigns of ℙ 1, Proceedings of the London Mathematical Society (3) 62 (1991), 469–489.

    Article  MATH  MathSciNet  Google Scholar 

  5. G. González-Díez, On prime Galois covers of the Riemann sphere, Annali di Matematica Pura ed Applicata 168 (1995), 1–15.

    Article  MATH  Google Scholar 

  6. W. J. Harvey, On branch loci in Teichmüller space, Transactions of the American Mathematical Society 153 (1971), 387–399.

    Article  MATH  MathSciNet  Google Scholar 

  7. A. Kontogeorgis, The group of automorphisms of cyclic extensions of rational function fields, Journal of Algebra 216 (1999), 665–706.

    Article  MATH  MathSciNet  Google Scholar 

  8. M. Schönert et al., GAP, Groups, Algorithms and Programming, Lehrstuhl D fur Mathematik, RWTH, Aachen, 4.0 ed, 2003.

    Google Scholar 

  9. David Singerman, Subgroups of Fuchsian groups and permutation groups, The Bulletin of the London Mathematical Society 2 (1970), 319–323.

    Article  MATH  MathSciNet  Google Scholar 

  10. G. Springer, Introduction to Riemann Surfaces, Addison-Wesley, Reading, MA, 1957.

    MATH  Google Scholar 

  11. M. Streit and J. Wolfart, Galois actions on some infinite series of Riemann surfaces with many automorphisms, Revista Matematica Complutense 13 (2000), 49–81.

    MATH  MathSciNet  Google Scholar 

  12. G. Toth, Finite Mobius Groups, Minimal Immersions of Spheres, and Moduli, Universitext, Springer, Berlin, 2002.

    Google Scholar 

  13. A. Wootton, Multiple prime covers of the riemann sphere, Central European Journal of Mathematics 3(2) (2005), 260–272.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wootton, A. Defining equations for cyclic prime covers of the Riemann sphere. Isr. J. Math. 157, 103–122 (2007). https://doi.org/10.1007/s11856-006-0004-4

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-006-0004-4

Keywords

Navigation