Totally invariant divisors of non trivial endomorphisms of the projective space

An F-space with Trivial Dual and Non-trivial Compact Endomorphisms

We give an example of an F-space which has non-trivial compact endomorphisms, but does not have any non-trivial continuous linear functionals.

Ruled Surfaces with Non-trivial Surjective Endomorphisms

Let X be a non-singular ruled surface over an algebraically closed field of characteristic zero. There is a non-trivial surjective endomorphism f : X → X if and only if X is (1) a toric surface, (2) a relatively minimal elliptic ruled surface, or (3) a relatively minimal ruled surface of irregularity greater than one which turns to be the product of P and the base curve after a finite étale bas...

Compact Complex Surfaces Admitting Non-trivial Surjective Endomorphisms

Smooth compact complex surfaces admitting non-trivial surjective endomorphisms are classified up to isomorphisms. The algebraic case has been classified in [3], [19]. The following surfaces are listed in the non-algebraic case: a complex torus, a Kodaira surface, a Hopf surface with at least two curves, an Inoue surface with curves, and an Inoue surface without curves satisfying a rationality c...

On endomorphisms of projective bundles

Let X be a projective bundle. We prove that X admits an endomorphism of degree > 1 and commuting with the projection to the base, if and only if X trivializes after a finite covering. When X is the projectivization of a vector bundle E of rank 2, we prove that it has an endomorphism of degree > 1 on a general fiber only if E splits after a finite base change. It is clear that, for a complex pro...

Smooth Divisors of Projective Hypersurfaces