This questions if related to a cute article of Beauville where he proves in particular the following theorem:

http://math1.unice.fr/~beauvill/pubs/endo.pdf

**Theorem.**− A smooth complex projective hypersurface of dimension $\ge 2$ and degree $\ge 3$ admits no endomorphism of degree $>1$.

Here "endomorphism" means a holomorphic self-map and the proof of the theorem uses algebraic geometry bien sure:) . But the following question is not mentioned in the article:

Question. What are smooth complex projective hypersufaces in $\mathbb CP^n$ that admit topological self-maps of degree $>1$?

I wonder if this question is trivial and completely answered for $n>2$?

This questions if related to a cute article of Beauville where he proves in particular the following theorem:

http://math1.unice.fr/~beauvill/pubs/endo.pdf

**Theorem.**− A smooth complex projective hypersurface of dimension $\ge 2$ and degree $\ge 3$ admits no endomorphism of degree $>1$.

Here "endomorphism" means a holomorphic self-map and the proof of the theorem uses algebraic geometry bien sure:) . But the following question is not mentioned in the article:

Question. What are smooth complex projective hypersufaces in $\mathbb CP^n$ that admit topological self-maps of degree $>1$?

I wonder if this question is trivial and completely answered for $n>2$?

Added. The comment of algori settles this question (apperently). But still I wonder for example how one can construct a self-map of a quintic in $\mathbb CP^3$ of degree $>1$.

This questions if related to a cute article of Beauville where he proves in particular the following theorem:

http://math1.unice.fr/~beauvill/pubs/endo.pdf

**Theorem.**− A smooth complex projective hypersurface of dimension $\ge 2$ and degree $\ge 3$ admits no endomorphism of degree $>1$.

The prove uses algebraic geometry bien sure:) and the following question is not mentioned in the article:

Question. What are smooth complex projective hypersufaces in $\mathbb CP^n$ that admit topological self-maps of degree $>1$?

I wonder if this question is trivial and completely answered for $n>2$?

This questions if related to a cute article of Beauville where he proves in particular the following theorem:

http://math1.unice.fr/~beauvill/pubs/endo.pdf

**Theorem.**− A smooth complex projective hypersurface of dimension $\ge 2$ and degree $\ge 3$ admits no endomorphism of degree $>1$.

Here "endomorphism" means a holomorphic self-map and the proof of the theorem uses algebraic geometry bien sure:) . But the following question is not mentioned in the article:

Question. What are smooth complex projective hypersufaces in $\mathbb CP^n$ that admit topological self-maps of degree $>1$?

I wonder if this question is trivial and completely answered for $n>2$?