Exceptional points of an endomorphism of the projective plane

E. Amerik; F. Campana

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arXiv · math/0310228

Exceptional points of an endomorphism of the projective plane

E. Amerik·F. Campana

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Abstract

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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BibTeX RIS

E. Amerik, F. Campana. 2003-10-15. Exceptional points of an endomorphism of the projective plane. https://arxiv.org/abs/math/0310228

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