Singularity of cubic hypersurfaces and hyperplane sections of projectivized tangent bundle of projective space
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917266889637888 |
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| author | Bansal, Ashima Sarkar, Supravat Vats, Shivam |
| author_facet | Bansal, Ashima Sarkar, Supravat Vats, Shivam |
| contents | 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 $2$. This also simplifies and extends recent results of Mazouni-Nagaraj in higher dimensions. We also compute the Chow ring of these hyperplane sections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10517 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Singularity of cubic hypersurfaces and hyperplane sections of projectivized tangent bundle of projective space Bansal, Ashima Sarkar, Supravat Vats, Shivam Algebraic Geometry 14B05, 14J17, 32S25 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 $2$. This also simplifies and extends recent results of Mazouni-Nagaraj in higher dimensions. We also compute the Chow ring of these hyperplane sections. |
| title | Singularity of cubic hypersurfaces and hyperplane sections of projectivized tangent bundle of projective space |
| topic | Algebraic Geometry 14B05, 14J17, 32S25 |
| url | https://arxiv.org/abs/2602.10517 |