On Macbeath-Singerman symmetries of Belyi surfaces with PSL(2,p) as a group of automorphisms

• Autorzy: Ewa Tyszkowska
• Języki publikacji: EN

Abstrakty

EN

The famous theorem of Belyi states that the compact Riemann surface X can be defined over the number field if and only if X can be uniformized by a finite index subgroup Γ of a Fuchsian triangle group Λ. As a result such surfaces are now called Belyi surfaces. The groups PSL(2,q),q=p n are known to act as the groups of automorphisms on such surfaces. Certain aspects of such actions have been extensively studied in the literature. In this paper, we deal with symmetries. Singerman showed, using acertain result of Macbeath, that such surfaces admit a symmetry which we shall call in this paper the Macbeath-Singerman symmetry. A classical theorem by Harnack states that the set of fixed points of a symmetry of a Riemann surface X of genus g consists of k disjoint Jordan curves called ovals for some k ranging between 0 and g+1. In this paper we show that given an odd prime p, a Macbetah-Singerman symmetry of Belyi surface with PSL(2,p) as a group of automorphisms has at most

Słowa kluczowe

EN

Riemann surface; automorphism; symmetry; ovals; minimum genus action; finite projective special linear groups; MSC (2000); Primary; 30F20; 30F50; Secondary; 14H37; 20H30; 20H10

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 2
• Strony: 208-220

Daty

wydano

2003-06-01

online

2003-06-01

Twórcy

autor

Ewa Tyszkowska

• University of Gdańsk

Bibliografia

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• [8] A. Harnack: “Uber die Vieltheiligkeit der ebenen algebraischen Kurven”, Math. Ann., Vol. 10, (1876), pp. 189–199. http://dx.doi.org/10.1007/BF01442458
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• [12] C.H. Sah: “Groups related to compact Riemann surfaces”, Acta Math, Vol. 123, (1969), pp. 13–42. http://dx.doi.org/10.1007/BF02392383
• [13] D. Singerman: “Symmetries of Riemann surfaces with large automorphism group”, Math. Ann., Vol. 210, (1974), pp. 17–32. http://dx.doi.org/10.1007/BF01344543
• [14] D. Singerman: “On the structure of non-euclidean crystallographic groups”, Proc. Camb. Phil. Soc., Vol. 76, (1974), pp. 233–240. http://dx.doi.org/10.1017/S0305004100048891

Identyfikatory

DOI

10.2478/BF02476009