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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.21518 |
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| _version_ | 1866917419730075648 |
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| author | Liu, Si-Yang Zhang, Yilong |
| author_facet | Liu, Si-Yang Zhang, Yilong |
| contents | For a smooth projective variety $X\subseteq \mathbb P^N$ over an algebraically closed field of char $0$, we show that the discriminant locus of a generic projection of $X$ is projectively dual to a general linear section of the dual variety, and deduce a purity statement for the discriminant. Over $\mathbb C$, we also show that the fundamental group of the complement of the branch divisor arising from generic projection of a normal hypersurface surjects onto a braid group via braid monodromy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21518 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the discriminant locus of a generic projection Liu, Si-Yang Zhang, Yilong Algebraic Geometry 14N05, 14C21, 14F35 For a smooth projective variety $X\subseteq \mathbb P^N$ over an algebraically closed field of char $0$, we show that the discriminant locus of a generic projection of $X$ is projectively dual to a general linear section of the dual variety, and deduce a purity statement for the discriminant. Over $\mathbb C$, we also show that the fundamental group of the complement of the branch divisor arising from generic projection of a normal hypersurface surjects onto a braid group via braid monodromy. |
| title | On the discriminant locus of a generic projection |
| topic | Algebraic Geometry 14N05, 14C21, 14F35 |
| url | https://arxiv.org/abs/2603.21518 |