I am looking for a (hopefully simple) example of a Calabi-Yau threefold (projective, simply connected, with trivial canonical bundle) admitting an automorphism of infinite order.



Calabi-Yau threefold with an automorphism of infinite order
A Schoen manifold $X$ is a generic complete intersection in $\mathbb{P}^2 \times \mathbb{P}^2 \times \mathbb{P}^1 $ of two hyper-surfaces of degree (3,0,1) and (0,3,1) respectively. Alternately, you can describe this Calabi-Yau threefold as the fiber product of two generic rational elliptic surfaces $X = S\times \_{\mathbb{P}^1} S'$ where $S$ and $S'$ are hyper-surfaces in $\mathbb{P}^2\times \mathbb{P}^1$ of degree (3,1) and projection to $\mathbb{P}^1$ induces the elliptic fibration. The surface $S$ has an infinite automorphism given by fiberwise addition by a non-zero section $\sigma: \mathbb{P}^1 \to S$ and this induces an infinite automorphism on $X$.


