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We study the polynomial fibration induced by the equation of the Kleinsurfaces obtained as quotient of finite linear groups of automorphisms of theplane; this surfaces are of type A, D, E, corresponding to their singularities.  The generic fibre of the polynomial fibration is a surface defined over thefunction field of the line. We proved that it is not rational in cases D, E,although it is obviously rational in the case A.  The group of automorphisms of the Klein surfaces is also described, and islinear and of finite dimension in cases D, E; this result being obviously falsein case A.

Non-rationality of some fibrations associated to Klein surfaces