IUMJ

Title: On fixed points of rational self-maps of complex projective plane

Authors: S. Ivashkovich

Issue: Volume 60 (2011), Issue 3, 803-812

Abstract:

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 $\mathbb{P}^2$.