Bloch’s Principle for Holomorphic Maps into Subvarieties of Semi-Abelian Varieties
Abstract
We generalize a fundamental theorem in higher-dimensional value distribution theory about entire curves in subvarieties X of semi-abelian varieties to the situation of the sequences of holomorphic maps from the unit disc into X . This generalization implies, among other things, that subvarieties of log general type in semi-abelian varieties are pseudo-Kobayashi hyperbolic. As another application, we improve a classical theorem due to Cartan in the 1920s about the system of nowhere vanishing holomorphic functions on the unit disc satisfying Borel’s identity.
Fields of Study & Subjects
Meromorphic and Entire Functions
Algebraic Geometry and Number Theory
Holomorphic and Operator Theory
Publication details
- Journal / source
- Publications of the Research Institute for Mathematical Sciences
- Volume
- 62
- Issue
- 3
- Pages
- 455–628
- Publication date
- 21 July 2026
- Language
- EN