Threefolds containing all curves are rationally connected
Abstract
Any smooth projective curve embeds into P 3 . More generally, any curve embeds into a rationally connected variety of dimension at least three. We prove conversely that if every curve embeds in a variety X , then X contains a rationally connected subvariety of dimension at least three. In particular, “all curves embed” is a birational property for threefolds.
Fields of Study & Subjects
Computational Geometry and Mesh Generation
Geometric and Algebraic Topology
Advanced Numerical Analysis Techniques
Publication details
- Journal / source
- Journal of Algebra
- Volume
- 713
- Pages
- 227–235
- Publication date
- 11 August 2026
- Language
- EN