A note related to Severi’s finiteness theorem
Abstract
In this short note, we show that there is a smooth projective surface which dominates infinitely many isomorphism classes of normal projective hyperbolic surfaces of general type. This shows the limitations in extending Severi’s classical finiteness theorem for curves to higher-dimensional varieties. Our proof is constructive and relies on the birational geometry of surfaces.
Fields of Study & Subjects
Advanced Numerical Analysis Techniques
Polynomial and algebraic computation
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- Kyoto journal of mathematics
- Publisher
- Duke University Press
- Volume
- 66
- Issue
- 3
- Pages
- 655-661
- Publication date
- 28 May 2026
- Language
- EN