We show that there is a smooth complex projective variety, of any dimension greater than or equal to , whose automorphism group is discrete and not finitely generated. Moreover, this variety admits infinitely many real forms which are mutually nonisomorphic over . Our result is inspired by the work of Lesieutre and answers questions by Dolgachev, Esnault, and Lesieutre.
"A surface with discrete and nonfinitely generated automorphism group." Duke Math. J. 168 (6) 941 - 966, 15 April 2019. https://doi.org/10.1215/00127094-2018-0054