CURIOSITIES AT C-EFFECTIVE=1

The moduli space of all rational conformal quantum field theories with effective central charge c(eff) = 1 is considered. Whereas the space pf unitary theories essentially forms a manifold, the nonunitary ones form a fractal which lies dense in the parameter plane. Moreover, the points of this set are shown to be in one-to-one correspondence with the elements of the modular group for which an action on this set is defined.