Symmetrizer group of a projective hypersurface
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915104465879040 |
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| author | Hwang, Jun-Muk |
| author_facet | Hwang, Jun-Muk |
| contents | To each projective hypersurface which is not a cone, we associate an abelian linear algebraic group called the symmetrizer group of the corresponding symmetric form. This group describes the set of homogeneous polynomials with the same Jacobian ideal and gives a conceptual explanation of results by Ueda--Yoshinaga and Wang. In particular, the diagonalizable part of the symmetrizer group detects Sebastiani-Thom property of the hypersurface and its unipotent part is related to the singularity of the hypersurface. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_08633 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symmetrizer group of a projective hypersurface Hwang, Jun-Muk Algebraic Geometry 14J70, 14J17 To each projective hypersurface which is not a cone, we associate an abelian linear algebraic group called the symmetrizer group of the corresponding symmetric form. This group describes the set of homogeneous polynomials with the same Jacobian ideal and gives a conceptual explanation of results by Ueda--Yoshinaga and Wang. In particular, the diagonalizable part of the symmetrizer group detects Sebastiani-Thom property of the hypersurface and its unipotent part is related to the singularity of the hypersurface. |
| title | Symmetrizer group of a projective hypersurface |
| topic | Algebraic Geometry 14J70, 14J17 |
| url | https://arxiv.org/abs/2501.08633 |