A surface with discrete and nonfinitely generated automorphism group

Abstract

We show that there is a smooth complex projective variety, of any dimension greater than or equal to $2$, whose automorphism group is discrete and not finitely generated. Moreover, this variety admits infinitely many real forms which are mutually nonisomorphic over $\mathbb{R}$. Our result is inspired by the work of Lesieutre and answers questions by Dolgachev, Esnault, and Lesieutre.