  Quotients $Y=X/conj$ by the complex conjugation $conj\: X\to X$ for complex
surfaces $X$ defined over $\R$ tend to be completely decomposable when they are
simply connected, i.e., split into connected sums $\#_n CP^2\#_m\barCP^2$ if
$w_2(Y)\ne0$, or into $\#_n(S^2\times S^2)$ if $w_2(Y)=0$. The author proves
this property for complete intersections which are constructed by method of a
small perturbation.
