Exceptional points of an endomorphism of the projective plane

Details Exceptional points of an endomorphism of the projective plane Exceptional points of an endomorphism of the projective plane

2003-10-15

arxiv.org/abs/math/0310228v1

Mathematics

Algebraic Geometry

15 pages, LaTeX

Scientific paper

let f be an endomorphism of a complex projective space, of degree bigger than one. Let us call an algebraic subset exceptional for f, if its inverse image is set-theoretically equal to itself. J.-Y. Briend, S. Cantat and M. Shishikura proved that an irreducible set like this is a linear subspace. In this paper, we obtain a bound for the number of codimension-two exceptional subspaces. In particular, we show that an endomorphism of the projective plane can be completely ramified at nine points at most.

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