Endomorphisms of Smooth Projective 3-Folds with Non-Negative Kodaira Dimension

Abstract

Let $X$ be a nonsingular projective 3-fold with non-negative Kodaira dimension $\kappa (X)\ge 0$ which admits a nonisomorphic surjective morphism $f:X\to X$ onto itself. If $\kappa (X)=0$ or $2$, a suitable finite étale covering $\tilde{X}$ of $X$ is isomorphic to an abelian 3-fold or the direct product $E\times S$ of an elliptic curve $E$ and a nonsingular algebraic surface $S$ with $\kappa (S)=\kappa (X)$.