Finite groups and complex projective surfaces

2025/12/22 by Alexander Lubotzky, Lubotzky, Alexander, Matthew Stover +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Analytic and geometric function theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals

paper · doi:10.48550/arxiv.2512.19505

openalex publication_date 2025/12/22 · openalex created_date 2025/12/24 · openalex updated_date 2026/07/28

Abstract

In response to a question raised by Belolipetsky and the first author, we prove that for every finite group G there are infinitely many isomorphism classes of compact complex hyperbolic 2-manifolds with automorphism group isomorphic to G.

Citations

• Profinite rigidity of Kähler groups: Riemann surfaces and subdirect products
• Arithmeticity, superrigidity and totally geodesic submanifolds of complex hyperbolic manifolds
• Hurwitz ball quotients
• Residual p properties of mapping class groups and surface groups
• Finite subgroups of the plane Cremona group

Cited by

• Normalizers of lattices and isometry groups of arithmetic hyperbolic manifolds

Related

• Hyperbolic 2-dimensional manifolds with 3-dimensional automorphism groups
• Finite groups acting on compact complex parallelizable manifolds
• Geometrical finiteness for automorphism groups via cone conjecture
• Complex-analytic intermediate hyperbolicity, and finiteness properties
• Realisation of groups as automorphism groups in categories