Singularity of cubic hypersurfaces and hyperplane sections of projectivized tangent bundle of projective space
Abstract
We show that the normal points of a cubic hypersurface in projective space have canonical singularities unless the hypersurface is an iterated cone over an elliptic curve. As an application, we give a simple linear algebraic description of all the hyperplane sections of projectivized tangent bundle of projective space, hence describing hyperplane sections of a rational homogeneous manifold of Picard rank 2 2 . This also simplifies and extends recent results of Mazouni-Nagaraj in higher dimensions. We also compute the Chow ring of these hyperplane sections.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Geometry and complex manifolds
Commutative Algebra and Its Applications
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Volume
- 154
- Issue
- 3
- Pages
- 975–987
- Publication date
- 15 January 2026
- Language
- EN