Multiple prime covers of the riemann sphere

• Autorzy: Aaron Wootton
• Języki publikacji: EN

Abstrakty

EN

A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C q of prime order q such that X/C q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p.

Słowa kluczowe

EN

Automorphism group; compact Riemann surface; hyperelliptic curve; 14H30; 14H37; 30F10; 30F60; 20H10

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 2
• Strony: 260-272

Daty

wydano

2005-06-01

online

2005-06-01

Twórcy

autor

Aaron Wootton

• University of Arizona

Bibliografia

• [1] R.D.M. Accola: “Strongly Branched Covers of Closed Riemann Surfaces”, Proc. of the AMS, Vol. 26(2), (1970), pp. 315–322. http://dx.doi.org/10.2307/2036396
• [2] R.D.M. Accola: “Riemann Surfaces with Automorphism Groups Admitting Partitions”, Proc. Amer. Math. Soc., Vol. 21, (1969), pp. 477–482. http://dx.doi.org/10.2307/2037029
• [3] T. Breuer: Characters and Automorphism Groups of Compact Riemann Surfaces, Cambridge University Press, 2001.
• [4] E. Bujalance, F.J. Cirre and M.D.E. Conder: “On Extendability of Group Actions on Compact Riemann Surfaces”, Trans. Amer. Math. Soc., Vol. 355, (2003), pp. 1537–1557. http://dx.doi.org/10.1090/S0002-9947-02-03184-7
• [5] A.M. Macbeath: “On a Theorem of Hurwitz”, Proceedings of the Glasgow Mathematical Association, Vol. 5, (1961), pp. 90–96. http://dx.doi.org/10.1017/S2040618500034365
• [6] B. Maskit: “On Poincaré's Theorem for Fundamental Polygons”, Advances in Mathematics, (1971), Vol. 7, pp. 219–230. http://dx.doi.org/10.1016/S0001-8708(71)80003-8
• [7] D. Singerman: “Finitely Maximal Fuchsian Groups”, J. London Math. Soc., Vol. 2 (6), (1972), pp. 29–38.
• [8] A. Wootton: “Non-Normal Belyî p-gonal Surfaces”, In: Computational Aspects of Algebraic Curves, Lect. Notes in Comp., (2005), to appear.
• [9] A. Wootton: “Defining Algebraic Polynomials for Cyclic Prime Covers of the Riemann Sphere”, Dissertation, (2004).

Identyfikatory

DOI

10.2478/BF02479202