A surface with discrete and non-finitely generated automorphism group

Abstract

We show that there is a smooth complex projective variety, of any dimension greater than or equal to two, whose automorphism group is discrete and not finitely generated. Moreover, this variety admits infinitely many real forms which are mutually non-isomorphic over the real number field. Our result is inspired by the work of Lesieutre and answers questions by Dolgachev, Esnault and Lesieutre.

final form to appear in Duke Math. J

References in corpus (1)

• Real structures on rational surfaces and automorphisms acting trivially on Picard groups

Cited by in corpus (1)

• Finiteness of Klein actions and real structures on compact hyperkähler manifolds