I‑AIMS Institute for Artificial Intelligence
and Mathematical Sciences
/

Cyclic curves over the reals

Milagros Izquierdo, Tanush Shaska

I-AIMS paper 2014-2 · Published in NATO Sci. Peace Secur. Ser. D Inf. Commun. Secur. 41 (2015), 70–83 · 2015

In this paper we study the automorphism groups of real curves admitting a regular meromorphic function f of degree p, so called real cyclic p-gonal curves. When p = 2 the automorphism groups of real hyperelliptic curves were given by Bujalance et al.

MSC classes: Primary 14H37; Secondary 14P05

PDF

References

  1. R. Accola, On cyclic trigonal Riemann surfaces. I, Trans. Amer. Math. Soc. 283 (1984), no. 2, 423–449. (85j:14052)
  2. G. Bartolini, A. Costa, and M. Izquierdo, On automorphisms groups of cyclic p-gonal Riemann surfaces, J. Symbolic Comput. 57 (2013), 61–69.
  3. S. A. Broughton, Superelliptic surfaces as p-gonal surfaces, Contemp. Math., vol. 629, Amer. Math. Soc., 2014.
  4. S. A. Broughton and A. Wootton, Exceptional automorphisms of super elliptic surfaces, Contemp. Math. 629 (2014), 29–42.
  5. E. Bujalance, F. J. Cirre, and G. Gromadzki, Groups of automorphisms of cyclic trigonal Riemann surfaces, J. Algebra 322 (2009), no. 4, 1086–1103. (2010k:14046)
  6. E. Bujalance, A. Costa, and D. Singerman, Application of Hoare’s theorem to symmetries of Riemann surfaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 18 (1993), no. 2, 307–322. (94i:20087)
  7. Emilio Bujalance, Francisco-Javier Cirre, J.-M. Gamboa, and Grzegorz Gromadzki, Symmetry types of hyperelliptic Riemann surfaces, Mem. Soc. Math. Fr. (N.S.) 86 (2001), vi+122. (2003d:30056)
  8. Emilio Bujalance, Jose J. Etayo, Jose M. Gamboa, and Grzegorz Gromadzki, Automorphism groups of compact bordered Klein surfaces, Lecture Notes in Mathematics, vol. 1439, Springer-Verlag, Berlin, 1990. A combinatorial approach. (92a:14018)
  9. A. Costa and M. Izquierdo, Symmetries of real cyclic p-gonal Riemann surfaces, Pacific J. Math. 213 (2004), no. 2, 231–243. (2004k:30098)
  10. ———, On real trigonal Riemann surfaces, Math. Scand. 98 (2006), no. 1, 53–68. (2007d:30029)
  11. A. Elezi and T. Shaska, Quantum codes from superelliptic curves, Albanian J. Math. 5 (2011), no. 4, 175–191.
  12. J. Gutierrez, D. Sevilla, and T. Shaska, Hyperelliptic curves of genus 3 with prescribed automorphism group, Computational aspects of algebraic curves, 2005, pp. 109–123. (2006j:14038)
  13. A. H. M. Hoare, Subgroups of N.E.C. groups and finite permutation groups, Quart. J. Math. Oxford Ser. (2) 41 (1990), no. 161, 45–59. (91d:20055)
  14. A. H. M. Hoare and D. Singerman, The orientability of subgroups of plane groups, Groups— St. Andrews 1981 (St. Andrews, 1981), 1982, pp. 221–227. (85g:20061)
  15. M. Izquierdo and D. Singerman, Pairs of symmetries of Riemann surfaces, Ann. Acad. Sci. Fenn. Math. 23 (1998), no. 1, 3–24. (98m:20065)
  16. A. Kontogeorgis, The group of automorphisms of cyclic extensions of rational function fields, J. Algebra 216 (1999), no. 2, 665–706. (2000f:12005)
  17. R. Sanjeewa, Automorphism groups of cyclic curves defined over finite fields of any characteristics, Albanian J. Math. 3 (2009), no. 4, 131–160. (2011a:14045)
  18. R. Sanjeewa and T. Shaska, Determining equations of families of cyclic curves, Albanian J. Math. 2 (2008), no. 3, 199–213. (2010d:14043)
  19. T. Shaska, Subvarieties of the hyperelliptic moduli determined by group actions, Serdica Math. J. 32 (2006), no. 4, 355–374. (2007k:14055)
  20. T. Shaska and F. Thompson, Bielliptic curves of genus 3 in the hyperelliptic moduli, Appl. Algebra Engrg. Comm. Comput. 24 (2013), no. 5, 387–412.
  21. A. Wootton, Defining equations for cyclic prime covers of the Riemann sphere, Israel J. Math. 157 (2007), 103–122. (2009b:30084)
  22. ———, The full automorphism group of a cyclic p-gonal surface, J. Algebra 312 (2007), no. 1, 377–396. (2008c:14043)

All preprints