The universal family of punctured Riemann surfaces is Stein
Abstract
Abstract We show that the universal Teichmüller family of compact Riemann surfaces of genus with punctures is a Stein manifold. We describe its basic function‐theoretic properties and pose some challenging questions. We show, in particular, that the space of fibrewise algebraic functions on the universal family is dense in the space of holomorphic functions, and that there is a fibrewise algebraic map of the universal family to a Euclidean space which restricts to a proper embedding on any fibre. We also obtain a relative Oka principle for holomorphic fibrewise algebraic maps of the universal family to any flexible algebraic manifold.
Fields of Study & Subjects
Analytic and geometric function theory
Holomorphic and Operator Theory
Geometric and Algebraic Topology
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 5
- Publication date
- 1 May 2026
- Language
- EN