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We determine all the Klein surfaces which have a cyclic automorphism group of the maximum possible order, and find their topological types. We also compute their full automorphism groups and show that, except for a finite number of exceptions, they coincide with the full automorphism groups of their Riemann double covers. Explicit algebraic equations of the surfaces and the formulae of their real forms and automorphisms are also given.  2004 Elsevier Inc. All rights reserved.

Abstract. It is well known that a generic compact Riemann surface of genus greater than two admits only the identity automorphism; however, examples of such Riemann surfaces with their defining algebraic equations have not appeared in the literature. In this paper we give the defining equations of a doubly infinite, two-parameter family of projective curves (Riemann surfaces if defined over the complex numbers), whose members admit only the identity automorphism.

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