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Invariant hypersurfaces of endomorphisms of the projective 3-space

By De-Qi Zhang

Abstract

We consider surjective endomorphisms f of degree > 1 on the projective n-space with n = 3, and f^{-1}-stable hypersurfaces V. We show that V is a hyperplane (i.e., deg(V) = 1) but with four possible exceptions; it is conjectured that deg(V) = 1 for any n > 1.Comment: 16 pages; submitted to The Proceedings of the Conference on Affine Algebraic Geometry, Osaka, March 2011, in honour of Prof M. Miyanish

Topics: Mathematics - Algebraic Geometry, Mathematics - Dynamical Systems, 37F10, 32H50, 14E20, 14J45
Year: 2011
OAI identifier: oai:arXiv.org:1104.1142
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