A surface with discrete and nonfinitely generated automorphism group (Q2631592)

It is known that the group of automorphisms of any \(K3\) surface is finitely generated. Inspired by the work of \textit{J. Lesieutre} [Invent. Math. 212, No. 1, 189--211 (2018; Zbl 1393.14012)], in the paper under review, the authors give an elegant example of a complex smooth surface birationally equivalent to a \(K3\) surface, whose group of automorphisms is not finitely generated. In their example, the surface is a suitable blowups of a certain Kummer surface with infinite group of automorphisms. Moreover they prove that such a surface admits infinitely many real forms which are mutually non-isomorphic over \(\mathbb{R}\), which answers a long-standing open question. Taking the product of such a surface with a smooth variety of general type, they obtain an example of a smooth variety of any dimension larger than two satisfying the above properties.