Abstract

Suppose X is a non-singular complex surface defined over \R, which is a complete intersection constructed by the method of a small perturbation, and Y=X/\conj is its quotient by the complex conjugation \conj\: X\to X. Assume that \conj has a fixed point. Then Y is completely decomposable, i.e., splits into a connected sum \#_n \Cp^2\#_m\barCP^2 or \#_n(S^2\!\times\! S^2).