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- David Corn, David Singerman
- Eur. J. Comb.
- 1988

Mathematics is full of dictionaries, one of the most well-thumbed being that between compact Riemann surfaces and complex algebraic curves; for example, branched coverings of surfaces and their groups of covering transformations can be translated into extensions of rational function fields and their Galois groups. An important problem is that of… (More)

- David Singerman, Robert I. Syddall
- 2003

In this work we explore the relationship between dessins and Riemann surfaces. From the work of Belyi and Grothendieck [1], [8], Jones/Singerman [10, 11], or Malgoire/Voisin [16], it follows that underlying a dessin H on a surface X, there is a canonical complex structure on X. This makes X into a Riemann surface R(H). In general, it is difficult to study… (More)

- Milagros Izquierdo, David Singerman
- Eur. J. Comb.
- 1994

- David Singerman
- 2008

We show that the least genus of any compact Riemann surface S, admitting a simple Suzuki group G = Sz(^) as a group of automorphisms, is equal to 1 +|G|/40. We compute the number of such surfaces S as the number of normal subgroups of the triangle group A(2,4,5) with quotient-group G, and investigate the associated regular maps of type {4,5}.

- Ioannis P. Ivrissimtzis, David Singerman
- Eur. J. Comb.
- 2005

Macbeath gave a formula for the number of fixed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe that this formula generalizes to determine the fixed-point set of each non-identity element of a cyclic group of… (More)

Macbeath gave a formula for the number of xed points for each non-identity element of a cyclic group of automorphisms of a compact Riemann surface in terms of the universal covering transformation group of the cyclic group. We observe that this formula generalizes to determine the xed-point set of each non-identity element of a cyclic group of automorphisms… (More)

- Cori Hypermaps, Dessins d’Enfants, David Singerman, Jürgen Wolfart
- 2008

This paper explains some facts probably known to experts and implicitely contained in the literature about dessins d’enfants but which seem to be nowhere explicitely stated. The 1skeleton of every regular Cori hypermap is the Cayley graph of its automorphism group, embedded in the underlying orientable surface. Conversely, every Cayley graph of a finite… (More)