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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.25820 |
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| _version_ | 1866915524502355968 |
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| author | Chen, Rizeng Hong, Hoon Yang, Jing |
| author_facet | Chen, Rizeng Hong, Hoon Yang, Jing |
| contents | This paper investigates the stratification of the discriminant hypersurface associated with a univariate polynomial via the number of its distinct complex roots. We introduce two novel approaches different from the one based on subdiscriminants. The first approach stratifies the discriminant hypersurface by recursively removing all the lowest-order points, while the second one stratifies the discriminant hypersurface by recursively removing all the smooth points. Both approaches rely solely on the discriminant itself instead of using high-order subdiscriminants. These results offer new insights into the intrinsic geometry of the discriminant and its connection to root multiplicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_25820 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stratifying Discriminant Hypersurface Chen, Rizeng Hong, Hoon Yang, Jing Algebraic Geometry 14J17, 14M12 This paper investigates the stratification of the discriminant hypersurface associated with a univariate polynomial via the number of its distinct complex roots. We introduce two novel approaches different from the one based on subdiscriminants. The first approach stratifies the discriminant hypersurface by recursively removing all the lowest-order points, while the second one stratifies the discriminant hypersurface by recursively removing all the smooth points. Both approaches rely solely on the discriminant itself instead of using high-order subdiscriminants. These results offer new insights into the intrinsic geometry of the discriminant and its connection to root multiplicity. |
| title | Stratifying Discriminant Hypersurface |
| topic | Algebraic Geometry 14J17, 14M12 |
| url | https://arxiv.org/abs/2509.25820 |