Noboru Nakayama (RIMS, Kyoto Univ.)
Title: Normal projective surfaces admitting non-isomorphic
surjective endomorphisms.
Abstract:
Let $X$ be a normal compact complex Moishezon surface admitting
a non-isomorphic holomorphic surjective endomorphism $f \colon X \to X$.
In a recent preprint, I obtained several partial classification results
on such surfaces $X$: For example, if $X$ is irrational or
if the canonical divisor $K_X$ is pseudo-effective, then
one of the following conditions is satisfied:
There is a finite Galois covering $A \to X$ \'etale in
codimension one from an abelian surface $A$.
$X$ is a projective cone over an elliptic curve.
$X$ is a $\mathbb{P}^1$-bundle over an elliptic curve.
There is a finite Galois covering $C \times T \to X$
\'etale in codimension one for non-singular projective curves $C$ and
$T$ with genus $g(C) \leq 1$ and $g(T) \geq 2$.
Conversely, if one of the conditions above is satisfied, then $X$ admits
a non-isomorphic surjective endomorphism. As a consequence of the classification, we can prove that $X$ is always projective.
I will explain briefly the classification results in the preprint, and also some key ideas.