On fixed points of rational self-maps of complex projective plane S. Ivashkovich 37F1032D2032H04fixed pointrational mapmeromorphic map For any given natural $d \ge 1$ we provide examples of rational self-maps of complex projective plane $\mathbb{P}^2$ of degree $d$ without (holomorphic) fixed points. This makes a contrast with the situation in one dimension. We also prove that the set of fixed-point-free rational self-maps of $\mathbb{P}^2$ is closed (modulo "degenerate" maps) in some natural topology on the space of rational self-maps of $\mathbb{P}^2$. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4265 10.1512/iumj.2011.60.4265 en Indiana Univ. Math. J. 60 (2011) 803 - 812 state-of-the-art mathematics http://iumj.org/access/