Invariant hypersurfaces of endomorphisms of the projective 3-space

Details Invariant hypersurfaces of endomorphisms of the projective 3-space Invariant hypersurfaces of endomorphisms of the projective 3-space

2011-04-06

arxiv.org/abs/1104.1142v1

Mathematics

Algebraic Geometry

16 pages; submitted to The Proceedings of the Conference on Affine Algebraic Geometry, Osaka, March 2011, in honour of Prof M.

Scientific paper

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.

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