Abstract

In this note we consider a certain class of closed Riemann surfaces which are a natural generalization of the so called classical Humbert curves. They are given by closed Riemann surfaces S admitting H ≅ ℤ2 k as a group of conformal automorphisms so that S/H is an orbifold of signature (0, k + 1; 2,..., 2). The classical ones are given by k = 4. Mainly, we describe some of its generalities and provide Fuchsian, algebraic and Schottky descriptions. © 2008 The Hebrew University of Jerusalem.