Quotients by complex conjugation for real complete intersection surfaces

TL;DR

This paper investigates the topological structure of quotients of complex surfaces by complex conjugation, showing they decompose into standard connected sums under certain conditions, especially for complete intersections constructed via small perturbations.

Contribution

It proves that quotients of complex complete intersection surfaces by conjugation are decomposable into standard connected sums, extending understanding of their topological classification.

Findings

Quotients are decomposable into connected sums when simply connected.

Decomposition depends on the second Stiefel-Whitney class.

Results apply to complete intersections constructed by small perturbation.

Abstract

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.