ALGEBRAIC CURVES, RIEMANN SURFACES AND KLEIN SURFACES WITH NO NON-TRIVIAL AUTOMORPHISMS OR SYMMETRIES

The explicit defining equations of a new family of curves whose members have a trivial automorphism group are given. Each member is defined for characteristic zero and all but a finite number of characteristics greater than zero. This family, in conjunction with a previously appearing family of the author’s, provides explicit examples of algebraic curves which possess only the trivial automorphism for each genus greater than three. The family is then used to construct Riemann surfaces without anticonformal automorphisms and Klein surfaces with no non-trivial automorphisms.AMS 2000 Mathematics subject classification: Primary 14H37; 30F50; 30F99