Quotients by complex conjugation for real complete intersection surfaces

Abstract

Quotients $Y=X/conj$ by the complex conjugation $conjX\to X$ for complex surfaces $X$ defined over $\mathbb{R}$ tend to be completely decomposable when they are simply connected, i.e., split into connected sums $\#_n CP^2\#_m\barCP^2$ if $w_2(Y)\ne 0$, 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.

5 pages, AMS-TeX, no Figures