# Varieties with infinitely generated automorphism group

John Lesieutre has just sent me an exciting new preprint in which he constructs a smooth projective variety $X$ such that

1. $\text{Aut}(X)$ is discrete, and
2. $\text{Aut}(X)$ is not finitely generated.

Whether or not such varieties existed has been an open question (asked by many people) for a long time.