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

Details On fixed points of rational self-maps of complex projective plane On fixed points of rational self-maps of complex projective plane

2009-11-27

arxiv.org/abs/0911.5084v2

Mathematics

Complex Variables

8 pages, 1 figure. To appear in the Indiana University Mathematics Journal

Scientific paper

For any given natural $d\ge 1$ we provide examples of rational self-maps of complex projective plane $\pp^2$ 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 $\pp^2$ is closed (modulo "degenerate" maps) in some natural topology on the space of rational self-maps of $\pp^2$.

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