Minimal rational curves on complete symmetric varieties
Abstract
We describe the families of minimal rational curves on any complete symmetric variety, and the corresponding varieties of minimal rational tangents (VMRT). In particular, we prove that these varieties are homogeneous and that for non-exceptional indecomposable wonderful varieties, there is a unique family of minimal rational curves, and hence a unique VMRT. We relate these results to the restricted root system of the associated symmetric space.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Polynomial and algebraic computation
Publication details
- Journal / source
- Journal of Differential Geometry
- Publisher
- International Press of Boston
- Volume
- 132
- Issue
- 2
- Publication date
- 8 January 2026