WILD AUTOMORPHISMS OF COMPACT COMPLEX SPACES OF LOWER DIMENSIONS

The paper proves a sharp classification in dimension ≤2: a compact complex space with a wild automorphism is either a complex torus or an Inoue surface of type S(+)M, and in both cases the automorphism has zero entropy; explicit examples are given, including an Inoue S(+)M example (Example 4.3) and the torus case via Theorem 2.4’s characterization of wild translations . The candidate solution reaches the same classification and zero-entropy conclusions by different routes (e.g., using Katok to rule out positive entropy). However, it overstates the torus example in dimension 2: translation by a non-torsion point need not be wild unless the point generates the torus (Theorem 2.4), so that part requires correction. Aside from this fixable example-level slip and some sketchy exclusions (K3/Enriques), the model’s reasoning broadly matches the paper’s conclusions.