Lines highly tangent to a hypersurface
Abstract
We study spaces of lines that meet a smooth hypersurface X X in P n \mathbf {P}^n to high order. As an application, we give a polynomial upper bound on the number of planes contained in a smooth degree d d hypersurface in P 5 \mathbf {P}^5 and provide a proof of a result of Landsberg without using moving frames.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Combinatorial Mathematics
Polynomial and algebraic computation
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 3
- Pages
- 943–956
- Publication date
- 14 January 2026
- Language
- EN