Mirror configurations of points and lines and algebraic surfaces of degree four

We prove that mirror nonsingular configurations of m points and $n$ lines in $\mathbb RP^3$ exist only for $m\le3$, $n\equiv0$ or $1\pmod4$ and for $m=0$ or $1\pmod4$, $n\equiv0\pmod2$. In addition, we give an elementary proof of V. M. Kharlamov's well-known result saying that if a nonsingular surface of degree four in $\mathbb RP^3$ is noncontractible and has $M\ge5$ components, then it is nonmirror. For the cases $M=5, 6,7$ and $8$, Kharlamov suggested an elementary proof using an analogy between such surfaces and configurations of $M-1$ points and a line. Our proof covers the remaining cases $M=9,10$. Bibl. 5 titles.