Quasi-homogeneous singularities of projective hypersurfaces and Jacobian syzygies
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913848401854464 |
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| author | Andrade, Aline V. Beorchia, Valentina Dimca, Alexandru Miró-Roig, Rosa M. |
| author_facet | Andrade, Aline V. Beorchia, Valentina Dimca, Alexandru Miró-Roig, Rosa M. |
| contents | We prove an unexpected general relation between the Jacobian syzygies of a projective hypersurface $V\subset \mathbb{P}^n$ with only isolated singularities and the nature of its singularities. This allows to establish a new method for the identification of quasi-homogeneous hypersurface isolated singularities. The result gives an insight on how the geometry is reflected in the Jacobian syzygies and extends previous results of the first, second and last author for free and nearly free plane curves [1]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06290 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasi-homogeneous singularities of projective hypersurfaces and Jacobian syzygies Andrade, Aline V. Beorchia, Valentina Dimca, Alexandru Miró-Roig, Rosa M. Algebraic Geometry Commutative Algebra Primary 14H50, 14J10, Secondary 14B05, 13C14, 13D02, 32S25, 32S05 15A69 We prove an unexpected general relation between the Jacobian syzygies of a projective hypersurface $V\subset \mathbb{P}^n$ with only isolated singularities and the nature of its singularities. This allows to establish a new method for the identification of quasi-homogeneous hypersurface isolated singularities. The result gives an insight on how the geometry is reflected in the Jacobian syzygies and extends previous results of the first, second and last author for free and nearly free plane curves [1]. |
| title | Quasi-homogeneous singularities of projective hypersurfaces and Jacobian syzygies |
| topic | Algebraic Geometry Commutative Algebra Primary 14H50, 14J10, Secondary 14B05, 13C14, 13D02, 32S25, 32S05 15A69 |
| url | https://arxiv.org/abs/2502.06290 |