Invariant hypersurfaces of endomorphisms of the projective 3-space

摘要

We consider surjective endomorphisms f of degree > 1 on the projective n-space P~n 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 ≥ 2; cf. [7], [3].